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Question 141
If $$\sin\theta+\cos\theta=\sqrt{3}\cos(90-\theta)$$, then what is the value of $$\tan\theta$$ ?
Solution
Given : $$sin\theta+cos\theta=\sqrt3cos(90^\circ-\theta)$$
=>Â $$sin\theta+cos\theta=\sqrt3sin\theta$$
=> $$cos\theta=sin\theta(\sqrt3-1)$$
=> $$\frac{sin\theta}{cos\theta}=\frac{1}{\sqrt3-1}$$
=> $$tan\theta=\frac{1}{\sqrt3-1}\times\frac{\sqrt3+1}{\sqrt3+1}$$
=> $$tan\theta=\frac{\sqrt3+1}{3-1}$$
=> $$tan\theta=\frac{\sqrt3+1}{2}$$
=> Ans - (C)
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