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Let f(x) = cotx/(1 + cotx) and a + b = 5(pi)/4, f(a).f(b) = pls explain..........

Let f(x) = cotx/(1 + cotx) and a + b = 5(pi)/4,


f(a).f(b) =


 


pls explain..........

Grade:12

1 Answers

RATHAN KUMAR
14 Points
10 years ago

Ans:1/2. EASY FRIEND...

f(a).f(b)=(cosa)/(cosa+sina)X(cosb)/(cosb+sinb),,,,on multiplying the denominator;

=(cosa.cosb)/{(cosa.cosb)+(sina.sinb)+(cosa.sinb+sina.cosb)}

On subtituing,,,,2(cosa.cosb)=cos(a+b)+cos(a-b), 2(sina.sinb)=cos(a-b)-cos(a+b) and the formula;sin(a+b),,you get one expression.On cancelling two terms you get,

=[cos(a+b)+cos(a-b)]/2[cos(a-b)+sin(a+b)]

here in numerator and denominator,cos(a+b)=sin(a+b)=(-1/2).

thus on cancelling numerator and denominator,you get answer as (1/2).

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