Question 53

What is the value of $$[(\sin 59$$° $$\cos 31$$° + $$\cos 59$$° $$\sin 31$$°) $$\div$$ ($$\cos 20$$° $$\cos 25$$° - $$\sin 20$$° $$\sin 25$$°$$)]$$?

Solution

sinAcosb + sinBcosA= sin(A+B)

cosAcosB - cosAcosB= cos(A+B)

So, $$sin(A+B)\div cos(A-B)=sin(59+31)\div cos(25+20)$$= $$sin 90\div cos 45$$= $$1\div1\div\sqrt{2}=\sqrt{2}$$

Therefore, Option D is correct.

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