Trigonometry Practice Test 2

Question : 17 of 22

Marks: +1, -0

If sin A + cos B = x and cos A + sin B = y, what is the value of sin A cos B + cos A sin B?

Solution:

sin A + cos = x and cos A + sin B = y
On squaring (i) and (ii) and then adding, we get

( \sin A + \cos B )^2+(\cos A + \sin B)^2=x^2+y^2

⇒\sin^2A+\cos^2B+2\sin A\cos B+\cos^2A+\sin^2B+2\sin B\cos A=x^2+y^2

⇒2(\sin A\cos A+\cos A\sin B)=x^2+y^2-2

⇒\sin A\cos A+\cos A\sin B={x^2+y^2-2}/2

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