Question 139

The numerical value of $$\frac{1}{1+\cot^{2}\theta}+\frac{3}{1+\tan^{2}\theta}+2\sin^{2}\theta$$ is

Solution

$$\frac{1}{1+\cot^{2}\theta}+\frac{3}{1+\tan^{2}\theta}+2\sin^{2}\theta$$

We know that ,

$$1 + cot^2 \theta$$ = $$cosec^2 \theta$$

$$1 + tan^2 \theta$$ = $$sec^2 \theta$$

$$\frac{1}{cosec^2 \theta}$$ + $$\frac{3}{sec^2 \theta}$$ + 2$$sin^2 \theta$$

$$sin^2 \theta + 2sin^2 \theta + 3cos^2 \theta$$

3( $$(sin^2 \theta + cos^2 \theta)$$) = 3

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