Q21 of 76 Page 52

If cos (θ + ϕ) = m cos (θ – ϕ), then prove that

[Hint: Express and apply Componendo and Dividendo]


Correction required: prove that:

Given,


cos (θ + ϕ) = m cos (θ – ϕ)


To prove:


∵ cos (θ + ϕ) = m cos (θ – ϕ)


⇒


Applying componendo – dividend, we get


⇒


From transformation formula, we know that –


cos(A+B) + cos(A – B) = 2cosAcosB


cos(A – B) – cos(A + B) = 2sinA sinB


⇒


⇒ {∵ (cos θ)/(sin θ) = cot θ }


⇒


⇒


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