Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that: ${\sin ^2}\frac{\pi }{6} + {\cos ^2}\frac{\pi }{3} - {\tan ^2}\frac{\pi }{4} = - \frac{1}{2}$
✓

Answer

We have
L.H.S. $ = {\sin ^2}\frac{\pi }{6} + {\cos ^2}\frac{\pi }{3} - {\tan ^2}\frac{\pi }{4}$
$ = {\left( {\frac{1}{2}} \right)^2} + {\left( {\frac{1}{2}} \right)^2} - {(1)^2}$$ = \frac{{1 + 1 - 4}}{4} = \frac{{ - 2}}{4}$
$ = \frac{{ - 1}}{2}$ RHS

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A committee of two person is selected from two men and two women. what is the probebility that the committee will have,
  1. No man?
  2. One Man?
  3. Two men?
→
Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow0^+}\frac{1}{3\text{x}}.$
→
Prove that:
$\frac{\cos2\text{x}}{1+\sin2\text{x}}=\tan(\frac{\pi}{4}-\text{x})$
→
Write the range of the function $f(x)=\sin [x]$, where $\frac{-\pi}{4} \leq x \leq \frac{\pi}{4}$.
→

Find the middle term in the expansion of:

$\Big(\text{x}^2-\frac{2}{\text{x}}\Big)^{10}$

→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$
→
A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
→
In what ratio is the line joining the points (2, 3) and (4, -5) divided by the line passing through the points (6, 8) and (-3, -2).
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\log\text{(3}+\text{x})-\log\text{(3}-\text{x})}{\text{x}}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos2\text{x}}{3\tan^2\text{x}}$
→