Saket Sharma Solutions for Exercise 1: Exercise 1

The value of ${\left(\frac{\sin 27°}{\cos 63°}\right)}^2+{\left(\frac{\cos 63°}{\sin 27°}\right)}^2-2\sin 30°$ is:

The value of the expression $[\mathrm{cosec} (75° + \mathrm{\theta }) – \sec (15° – \mathrm{\theta }) – \tan (55° + \mathrm{\theta }) + \cot (35° – \mathrm{\theta }\left)\right]$ is ______

If $\tan (x + y) \tan (x - y) = 1$, then the value of  $\tan \left(\frac{2x}{3}\right)$ is_____.

If $0\le \mathrm{\theta }\le \frac{\mathrm{\pi }}{2}$, $2\mathrm{y} \cos \theta = \mathrm{x} \sin \theta$ and$2\mathrm{x} \sec \theta -\mathrm{y} \mathrm{cosec} \theta =3$, then the value of${\mathrm{x}}^2 + 4{\mathrm{y}}^2$ is_____.

If $5\tan \theta = 4$ , then the value of$\left(\frac{5sin\theta -3cos\theta }{5sin\theta +3cos\theta }\right)$  is_____.

The value of $\frac{{\displaystyle \frac{1+{\sin }^2(\theta +16)}{1+{\sin }^2(\theta +31)}\times \frac{{\cos }^2(\theta +46)+{\cos }^2(\theta +16)}{\cos e{c}^2(\theta +76)+\cos e{c}^2(\theta +76)}}}{\sin (\theta +46)\times \tan (\theta +46)}$

where $\theta =14°$ is.

The value of $1+\frac{{\sin }^{2}23}{{\cos }^{2}23}-\frac{{\cos }^{2}67}{{\sin }^{2}67}+\frac{\cos e{c}^{2}67}{se{c}^{2}23}$ is-

The simplest value of ${\sin }^{2}x+2{\tan }^{2}x-2{\sec }^{2}x+{\cos }^{2}x$ is_____.