InterviewSolution
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InterviewSolution
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If `cosx-sinalphacotbetasinx=cosa ,`then the value of `tan(x/2)`is`-tan(alpha/2)cot(beta/2)`(b) `tan(alpha/2)tan(beta/2)``-cot((alphabeta)/2)tan(beta/2)`(d) `cot(alpha/2)cot(beta/2)`A. `-tan (alpha2)cot(beta2)`B. `tan (alpha//2)tan(beta//2)`C. `-cot(alpha//2)tan(beta//2)`D. `cot(alpha//2)cot(beta//2)` |
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Answer» Correct Answer - A::B `cos x - sin alpha cos beta sinx = cos alpha ` `rArr (1-tan^(2)(x//2))/(1+tan^(2)(x//2)) - sin alpha cos beta (2tan(x//2))/(1+tan^(2)(x//2)) = cos alpha` `rArr tan^(2) ""(x)/(2) (1+ cosalpha ) + 2 sin alpha cos beta tan ""(x)/(2) - (1- cos alpha) =0` `rArr tan ^(2)""(x)/(2) + (2sinalpha cos beta)/(1+ cos alpha) tan""(x)/(2) - (1-cos alpha)/( 1+cos alpha) =0` `rArr tan^(2)""(x)/(2) + 2 tan""(alpha)/(2) cos beta tan ""(x)/(2) - tan^(2) ""(alpha)/(2)=0` `rArr tan^(2""(x)/(2) + 2 tan""(alpha)/(2)*(1)/(2)(cot""( beta)/(2) - tan ""(beta)/(2)) tan ""(x)/(2) - tan^(2) (alpha)/(2) =0` `rArr (tan ""(x)/(2) + cot""(beta)/(2) tan""(alpha)/(2)) (tan""(x)/(2) - tan""(beta)/(2) tan""(alpha)/(2)) =0` `rArr tan((x)/(2)) = - tan((alpha)/(2)) cot((beta)/(2))` or `" " tan ((x)/(2)) = tan((alpha)/(2) tan((beta)/(2))` |
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