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Maths-

General

Easy

Question

if $A equals 340 to the power of ring operator$ then $square root of 1 minus sin space A end root minus square root of 1 plus sin space A end root equals$

$2 \cos A / 2$
$2 \sin A / 2$
$- 2 \cos A / 2$
$- 2 \sin A / 2$

The correct answer is: $2 sin space A divided by 2$

Step by step solution:
$square root of 1 minus sin space A end root$ $negative square root of 1 plus sin space A end root equals$ $square root of sin squared A over 2 plus cos squared A over 2 minus 2 sin A over 2 cos A over 2 end root$ $negative square root of sin squared A over 2 plus cos squared A over 2 plus 2 sin A over 2 cos A over 2 end root$
$equals square root of open parentheses sin A over 2 minus cos A over 2 close parentheses squared end root$ $negative square root of open parentheses sin A over 2 plus cos A over 2 close parentheses squared end root$
$equals open vertical bar sin A over 2 minus cos A over 2 close vertical bar$ $negative open vertical bar sin A over 2 plus cos A over 2 close vertical bar$
$equals open vertical bar sin space 170 degree minus cos space 170 degree close vertical bar$ $negative open vertical bar sin space 170 degree plus cos space 170 degree close vertical bar$
$equals open vertical bar negative sin 10 degree minus cos 10 degree close vertical bar$ $negative open vertical bar sin 10 degree minus cos 10 degree close vertical bar$
$equals sin space 10 degree space plus space cos space 10 degree$ $plus sin space 10 degree minus space cos space 10 degree$
$equals 2 space sin space 10 degree$ $equals space 2 space sin space 170 degree$ $equals space 2 space sin space 340 over 2 to the power of degree$
$equals space 2 space sin space A over 2$
Hence, option(a) is the correct option.

Related Questions to study

$2 sin space A over 2 equals square root of 1 plus sin space A end root minus square root of 1 minus sin space A end root text then end text$

$2 sin space A over 2 equals square root of 1 plus sin space A end root minus square root of 1 minus sin space A end root text then end text$

$I f space 2 cos space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

$I f space 2 cos space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

$I f space 2 sin space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

$I f space 2 sin space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

parallel

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parallel

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parallel

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STATEMENT-2: The determinant $open vertical bar table row 1 3 cell negative 1 end cell row cell negative 1 end cell cell negative 2 end cell k row 1 4 1 end table close vertical bar$ $not equal to$ 0, for k $not equal to$ 3

Consider the system of equations-x – 2y + 3z = –1–x + y – 2z = k x – 3y + 4z = 1
STATEMENT-1: The system of equations has no solution for k $not equal to$ 3
STATEMENT-2: The determinant $open vertical bar table row 1 3 cell negative 1 end cell row cell negative 1 end cell cell negative 2 end cell k row 1 4 1 end table close vertical bar$ $not equal to$ 0, for k $not equal to$ 3

Suppose, x > 0, y > 0, z > 0 and $capital delta$ (a, b, c) = $open vertical bar table row cell x log invisible function application 2 end cell 3 cell 15 plus log invisible function application left parenthesis a to the power of x end exponent right parenthesis end cell row cell y log invisible function application 3 end cell 5 cell 25 plus log invisible function application left parenthesis b to the power of y end exponent right parenthesis end cell row cell z log invisible function application 5 end cell 7 cell 35 plus log invisible function application left parenthesis c to the power of z end exponent right parenthesis end cell end table close vertical bar$
Statement - 1 : $capital delta$ (8, 27, 125) = 0
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Suppose, x > 0, y > 0, z > 0 and $capital delta$ (a, b, c) = $open vertical bar table row cell x log invisible function application 2 end cell 3 cell 15 plus log invisible function application left parenthesis a to the power of x end exponent right parenthesis end cell row cell y log invisible function application 3 end cell 5 cell 25 plus log invisible function application left parenthesis b to the power of y end exponent right parenthesis end cell row cell z log invisible function application 5 end cell 7 cell 35 plus log invisible function application left parenthesis c to the power of z end exponent right parenthesis end cell end table close vertical bar$
Statement - 1 : $capital delta$ (8, 27, 125) = 0
Statement - 2 : $capital delta$ $open parentheses fraction numerator 1 over denominator 2 end fraction comma fraction numerator 1 over denominator 3 end fraction comma fraction numerator 1 over denominator 5 end fraction close parentheses$ = 0

If $fraction numerator cos space x over denominator cos space y end fraction equals 2$ and $cos space left parenthesis x minus y right parenthesis equals fraction numerator square root of 3 over denominator 2 end fraction$ then y=

If $fraction numerator cos space x over denominator cos space y end fraction equals 2$ and $cos space left parenthesis x minus y right parenthesis equals fraction numerator square root of 3 over denominator 2 end fraction$ then y=

parallel

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