Question

prove that cos theta cos (90 - theta ) / cot (90 - theta = cos ^2 theta​

Answer 1

Answer:

Solution:

Prove that :

Cos theta. cos ( 90- theta )

____________ = cos ² theta

cot (90 - theta)

L.H.S = Cos theta . Cos ( 90 - theta)

_____________

cot ( 90 - theta)

= cos theta. sin theta

_______.......[since, cos(90- A) = sin A

tan theta cot ( 90 -A) = tan A]

= cos theta. sin theta

________

sin theta

________

cos theta

= cos theta. sin theta × cos theta

_______

sin theta

.

.........................[ since, a/ b / c/d = ad/ bc]

= cos theta × cos theta

= cos ² theta

= R.H.S

Therefore, L.H.S = R.H.S