Question 64

If $$4(\cosec^2 65^\circ - \tan^2 25^\circ) - \sin 90^\circ - \tan^2 63^\circ y \tan^2 27^\circ = \frac{y}{2}$$, then the value of $$y$$ is:

Solution

$$4(\cosec^2 65^\circ - \tan^2 25^\circ) - \sin 90^\circ - \tan^2 63^\circ y \tan^2 27^\circ = \frac{y}{2}$$

$$=$$> $$4(\operatorname{cosec}^265^{\circ}-\tan^2\left(90-65\right)^{\circ})-\left(1\right)-\tan^263^{\circ}y\tan^2\left(90-63\right)^{\circ}=\frac{y}{2}$$

$$=$$> $$4(\operatorname{cosec}^265^{\circ}-\cot^265)^{\circ\ }-1- \tan^263^{\circ}y\cot^263^{\circ}=\frac{y}{2}$$

$$=$$> $$4\left(1\right)-1-y=\frac{y}{2}$$

$$=$$> $$\frac{y}{2}+y=3$$

$$=$$> $$\frac{3y}{2}=3$$

$$=$$> $$y=2$$

Hence, the correct answer is Option A


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