Question 72

If $$7(\cosec^2 55^\circ - \tan^2 35^\circ) + 2 \sin 90^\circ - \tan^2 52^\circ y \tan^2 38^\circ = \frac{y}{2}$$, then the value of $$y$$ is:

Solution

$$7(\cosec^2 55^\circ - \tan^2 35^\circ) +2 \sin 90^\circ - \tan^2 52^\circ y \tan^2 38^\circ = \frac{y}{2}$$

$$=$$> $$7(\operatorname{cosec}^255^{\circ}-\tan^2\left(90-55\right)^{\circ})+2 \left(1\right)-\tan^252^{\circ}y\tan^2\left(90-52\right)^{\circ}=\frac{y}{2}$$

$$=$$> $$7(\operatorname{cosec}^255^{\circ}-\cot^255)^{\circ\ }+2- \tan^252^{\circ}y\cot^252^{\circ}=\frac{y}{2}$$

$$=$$> $$7\left(1\right)+2-y=\frac{y}{2}$$

$$=$$> $$\frac{y}{2}+y=9$$

$$=$$> $$\frac{3y}{2}=9$$

$$=$$> $$y=6$$

Hence, the correct answer is Option C


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