Q15 of 90 Page 8

If cos (α + β) sin (γ + δ) = cos (α - β) sin (γ - δ), prove that cot α cot β cot γ = cot δ

Given,


cos (α + β) sin (γ + δ) = cos (α - β) sin (γ – δ)



Adding 1 both sides:





Now,



Subtracting 1 both sides:





Dividing equation (i) by equation (ii):










{sin (-A) = -sin A & cos (-A) = cos A}




⇒ cot α cot β cot γ = cot δ


Hence Proved


More from this chapter

All 90 →
13

Prove that:

i.


ii. sin(B– C)cos(A – D) + sin(C – A)cos(B – D) + sin(A – B)cos(C – D) = 0

 14

prove that tan A tan B tan C tan D= -1

 16

If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y -x) cot θ

 17

If cos (A + B) sin (C – D) = cos (A – B) sin (C + D), prove that tan A tan B tan C + tan D = 0