If sec 15θ = cosec 15θ (0° < θ < 10°) then value of θ is

Question 37

Solution

Given : $$sec(15\theta)=cosec(15\theta)$$

=> $$\frac{1}{cos(15\theta)}=\frac{1}{sin(15\theta)}$$

=> $$\frac{sin(15\theta)}{cos(15\theta)}=1$$

=> $$tan(15\theta)=1$$

=> $$15\theta=tan^{-1}(1)$$

=> $$15\theta=45^\circ$$

=> $$\theta=\frac{45}{15}=3^\circ$$

=> Ans - (D)

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