If 3 sin 5cos 4 then what is the value of 3 cos minus 5 sin 2 ........

Quantitative Aptitude (CDS) Trignometry

If 3 sin $\Theta$ + 5cos $\Theta$ = 4, then what is the value of (3 cos $\Theta$ −5 sin $\Theta$ )²?

3 sin $\Theta$ + 5cos $\Theta$ = 4

if a sin $\Theta$ + bcos $\Theta$ = c then

$a cos\Theta -bsin\Theta =\pm \sqrt{a^{2}+b^{2}-c^{2}}$

Taking a = 3, b = 5 & c = 4, we get

$3 cos\Theta -5 sin\Theta = \sqrt{3^{2}+5^{2}-4^{2}}$ = $3 \sqrt{2}$

Squaring both sides

$(3cos\Theta -5sin\Theta )^{2}=(3 \sqrt{2})^{2}=18$

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