If (1 + \sin\alpha) (1 + \sin\beta) (1 + \sin\gamma) = (1 – \sin\alpha) (1 – \sin\beta)(1 – \sin\gamma) , then each side is equal to

Correct Answer is : ±cosαcosβcosγ

\pm\cos\alpha\cos\beta\cos\gamma

\pm\sin\alpha\sin\beta\sin\gamma

\pm\sin\alpha\cos\beta\cos\gamma

\pm\sin\alpha\sin\beta\cos\gamma

RRB Junior Engineer Stage 1 Model Papers 4

Question : 28 of 99

Marks: +1, -0

(1 + \sinα) (1 + \sinβ) (1 + \sinγ) = (1 – \sinα) (1 – \sinβ)(1 – \sinγ)

, then each side is equal to

Solution:

(1 + \sin α) (1 + \sin β) (1 + \sin γ) = (1 – \sin α) (1 –\sin β) (1 – \sin γ) = x

∴ x .x = (1 + \sin α) (1 – \sin α) (1 + \sin β) (1 – \sin β) (1+ \sin γ) (1 + \sin γ)

= (1 – \sin^2α) (1 – \sin^2β) (1 – \sin^2γ)

= \cos^2α. \cos^2β.\cos^2 γ

= x = ± \cosα.\cos β . \cosγ

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