If cos -a- sin -b- where - - 0- -2 then-

The correct options are A sin (α β)=ab √((1 a^2 b^2+a^2b^2)) B cos(α β)=a√((1 b^2))+b√((1 a^2)) Given cos (θ α)=a, sin (θ β)=b , where (θ α ...

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Trigonometric Ratios of Compound Angles

If cos θ-α=...

Question

If $cos (θ - α) = a, sin (θ - β) = b$ , where $(θ - α, θ - β) \in (0, \frac{π}{2})$ then-

sin (α - β) = a b - \sqrt{(1 - a^{2} - b^{2} + a^{2} b^{2})}

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cos (α - β) = a \sqrt{(1 - b^{2})} + b \sqrt{(1 - a^{2})}

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sin (α - β) = a b + \sqrt{(1 - a^{2} - b^{2} + a^{2} b^{2})}

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cos (α - β) = a \sqrt{(1 - b^{2})} - b \sqrt{(1 - a^{2})}

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\sin (α + β) = \frac{2 a b}{a^{2} + b^{2}}

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