JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Analyzing +4 | -1

Let

f(x)=1+2 \cos x+3 \sin x

. If

\alpha f(x)+\beta f(x-\gamma)=1

where

\alpha, \beta, \gamma \in R

holds for all

x \in R

, then

\frac{\beta \cos \gamma}{\alpha}

is equal to

View answer and explanation

Correct option: A

-1

Option A (-1) is correct because by finding f(x-π) and comparing αf(x) + βf(x-γ) = 1, we get α = β = 1/2 and γ = π, thus βcosγ/α = -1.

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