If 3 sin - - 5 cos - - 5- then 3 cos - - 5 sin - is equal to-

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Product of Trigonometric Ratios in Terms of Their Sum

If 3 sin β + ...

Question

$If 3 s i n β + 5 c o s β = 5, t h e n 3 c o s β - 5 s i n β$ is equal to?

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\frac{1}{3}

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α = {cos}^{- 1} (\frac{3}{5}), β = {tan}^{- 1} (\frac{1}{3}),

0 < α, β < \frac{π}{2},

α - β

α

β

c o s^{2} α + c o s^{2} β = 3 / 2

α

β

α + β

cos α + cos β = \frac{3}{2}

sin α + sin β = \frac{1}{2}

θ

α

β

sin 2 θ + cos 2 θ

If $s i n α, s i n β, c o s α$ are in GP, then roots of equation $x^{2} s i n β + 2 x c o s β + s i n β = 0$ are

s i n α = \frac{1}{\sqrt{5}} a n d s i n β = \frac{3}{5}, t h e n β - α

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