Question 142

If 29 tan θ = 31, then the value of $$\frac{1+2sin\theta cos\theta}{1-2\sin\theta\cos\theta}$$

Solution

29 tan θ = 31

sin θ/cos θ = 31/29

by C.D rule,

$$\frac{sinθ+cosθ}{sinθ-cosθ}=\frac{31+29}{31-29}=\frac{60}{2}=30$$

now,

$$\frac{1+2sin\theta cos\theta}{1-2\sin\theta\cos\theta}$$

= $$\frac{sin^{2}\theta+cos^{2}\theta+2sin\theta cos\theta}{sin^{2}\theta+cos^{2}\theta-2\sin\theta\cos\theta}$$

= $$\frac{(sin\theta+cos\theta)^{2}}{(sin\theta-\cos\theta)^{2}}$$

= $$30^{2}$$

= 900.

so the answer is option B.

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