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Maths-

General

Easy

Question

In a triangle ABC if cos A + 2cos B + cos C = 2, the sides of the triangle are in

HP
GP
AP
None of these

The correct answer is: AP

cos A + 2 cos B + cos C = 2
⇒ cos A + cos C = 2(1 – cos B)
$table row cell rightwards double arrow 2 c o s invisible function application open parentheses fraction numerator A plus C over denominator 2 end fraction close parentheses c o s invisible function application open parentheses fraction numerator A minus C over denominator 2 end fraction close parentheses equals 4 s i n to the power of 2 end exponent invisible function application fraction numerator B over denominator 2 end fraction end cell row cell rightwards double arrow c o s invisible function application fraction numerator A minus C over denominator 2 end fraction equals 2 s i n invisible function application fraction numerator B over denominator 2 end fraction end cell row cell rightwards double arrow c o s invisible function application fraction numerator A minus C over denominator 2 end fraction equals 2 c o s invisible function application fraction numerator A plus C over denominator 2 end fraction end cell row cell rightwards double arrow c o s invisible function application fraction numerator A over denominator 2 end fraction c o s invisible function application fraction numerator C over denominator 2 end fraction plus s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction equals 2 c o s invisible function application fraction numerator A over denominator 2 end fraction c o s invisible function application fraction numerator C over denominator 2 end fraction minus 2 s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction end cell row cell rightwards double arrow c o t invisible function application fraction numerator A over denominator 2 end fraction c o t invisible function application fraction numerator C over denominator 2 end fraction equals 3 end cell end table$
$table row cell rightwards arrow square root of fraction numerator s left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end fraction end root times square root of fraction numerator s left parenthesis s minus c right parenthesis over denominator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end fraction end root equals 3 end cell row cell rightwards double arrow fraction numerator s over denominator s minus b end fraction equals 3 rightwards double arrow 5 equals 3 s minus 3 b rightwards double arrow 2 s equals 3 b end cell row cell rightwards double arrow a plus c equals 2 b rightwards double arrow a comma b comma c blank a r e blank i n blank A P. end cell end table$

Related Questions to study

$I f blank x comma y comma z$ are perpendicular drawn from the vertices of a triangle having a, band c, then $fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction$ is equal to

$I f blank x comma y comma z$ are perpendicular drawn from the vertices of a triangle having a, band c, then $fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction$ is equal to

Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

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Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

Some alcohols . like $C H subscript 3 end subscript minus O H comma C F subscript 3 end subscript minus C H subscript 2 end subscript minus O H$ , $blank open parentheses C F subscript 3 end subscript close parentheses subscript 3 end subscript C minus O H$
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Which of the following will react fastest with sodium?

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