NCERT Solutions for Chapter: Trigonometric Functions, Exercise 1: EXERCISE

If $\cos (\alpha +\beta )=\frac{4}{5}$ and $\sin (\alpha -\beta )=\frac{5}{13}$, where $\alpha$ lie between $0$ and $\frac{\pi }{4},$ find the value of $\tan 2\alpha$.

If $\tan x=\frac{b}{a},$ then find the value of $\sqrt{\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}$.

If the value of $\tan 22°{30}^{\text{'}}$ is $\sqrt{m}-1$, then $m=$

Find the value of the expression $3\left[{\sin }^4\left(\frac{3\pi }{2}-\alpha \right)+{\sin }^4(3\pi +\alpha )\right]-2\left({\sin }^6\left(\frac{\pi }{2}+\alpha \right)+{\sin }^6(5\pi -\alpha )\right]$.

If $\theta$ lies in the first quadrant and $\cos \theta =\frac{8}{17},$ then find the value of $\cos \left(30°+\theta \right)+\cos \left(45°-\theta \right)+\cos \left(120°-\theta \right).$

Find the value of the expression ${\cos }^4\frac{\pi }{8}+{\cos }^4\frac{3\pi }{8}+{\cos }^4\frac{5\pi }{8}+{\cos }^4\frac{7\pi }{8}$.

If $\sin x+\cos x=a$, and $\left|\sin x-\cos x\right|=\sqrt{k-a^2}$, then $k=$ _____.

In a $△ABC$ with $\angle C=90°$ the equation whose roots are $\tan A$ and $\tan B$ is