Question

1/(tan theta+cot theta)=sin theta.cos theta prove it

Answer 1

Solution:

Here I am using A instead of theta.

LHS =1/(tanA+cotA)

= 1/[tanA+1/tanA]

/* cotA = 1/tanA */

= tanA/(tan²A+1)

= tanA/sec²A

/* 1+tan²A = sec²A */

= (sinA/cosA)/(1/cos²A)

= (sinA/cosA)×(cos²A/1)

= sinAcosA

= RHS

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