Question 140

The value of $$\frac{4}{1+\tan^{2}\alpha}+\frac{3}{1+\cot^{2}\alpha}+ \sin^{2}\alpha$$ is

Solution

we need to find the value of $$\frac{4}{1+\tan^{2}\alpha}+\frac{3}{1+\cot^{2}\alpha}+ \sin^{2}\alpha$$

We know that ,

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

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

Using above mentioned identities

$$\frac{4}{sec^2 \alpha}$$ + $$\frac{3}{cosec^2 \alpha}$$ + $$sin^2 \alpha$$

4$$cos^2 \alpha$$ + 4$$sin^2 \alpha$$

4($$cos^2 \alpha$$ + $$sin^2 \alpha)$$

=4

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