Question

If root 3 sin theta = cos theta, find value of. sin theta.tan theta (1+cot theta)/sin theta + cos theta

Answer 1

This is the answer.....

Answer 2

Given:

√3 sin theta = cos theta

=>(sin theta)/(cos theta)= 1/√3

=> tan theta = tan 30°

Therefore,

theta = 30° ----(1)

Now ,

Value of sin theta.tan theta (1+cot theta)/sin theta + cos theta

= [ sin30°tan30°(1+cot30°)]/(sin30°+cos30°)

= [(1/2)(1/√3)(1+√3)]/[1/2+√3/2]

= [1/(2√3)(1+√3)]/[(1+√3)/2]

After cancellation, we get

= 1/√3

Therefore,

Required value = 1/√3

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