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We have,
= tan θ = RHS
LHS,
= cot θ = RHS
= 2 cos θ = RHS
Dividing numerator and denomenator by cos θ
Dividing numerator and denominator by cos θ/2
= 2
= RHS
= 1 + 1
(cos λ + cos β)2 + (sin λ + sin β)2
= cos2 λ + cos2 β + 2 cos λ cos β + sin2 λ + sin2 β + 2 sin λ sin β
= (cos2 λ + sin2 λ) + (cos2 β + sin2 β) + 2(cos λ cos β + sin λ sin β)
= 1 + 1 + 2cos (λ - β)
= 2 + 2 cos (λ - β)
= 2(1 + cos (λ - β)
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Chapter 9: Trigonometric Ratios of Multiple and...