Maharashtra Board Solutions for Chapter: Trigonometry - 1, Exercise 3: MISCELLANEOUS EXERCISE - 2

State the quadrant in which $\theta$ lies if $\mathrm{sin\theta }<0$ and $\mathrm{cos\theta }<0$.

State the quadrant in which $\theta$ lies if $\mathrm{sin\theta }>0$ and $\mathrm{tan\theta }<0$.

Which is greater $\sin \left({1856}^0\right)$ or $\sin \left({2006}^0\right)$ ?

Which of the following is positive ? $\sin (-{310}^0)$ or $\sin \left({310}^0\right)$

Show that $1- 2\mathrm{sin\theta } \mathrm{cos\theta } \ge 0$ for all $\mathrm{\theta }\in R$.

Show that ${\tan }^2\theta +{\cot }^2\theta \ge 2$, for all $\theta \in R$.

If $\sin \theta =\frac{x^2-y^2}{x^2+y^2}$ then find the values of $\cos \theta , \tan \theta$ in terms of $x$ and $y$.

If $\mathrm{sec\theta }=\sqrt{2}$ and $\frac{3\mathrm{\pi }}{2}<\mathrm{\theta }<2\mathrm{\pi }$, then evaluate: $\frac{1+\mathrm{tan\theta }+\mathrm{cosec\theta }}{1+\mathrm{cot\theta }-\mathrm{cosec\theta }}$.