Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that: $\tan(-225^\circ)\cot(-405^\circ)-\tan(765^\circ)+\cot(675^\circ)=0$
✓

Answer

$\text{L.H.S}=\tan(-225^\circ)\cot(-405^\circ)-\tan(-765)\cot(675^\circ)$ $=-\tan225^\circ(-\cot405^\circ)+\tan765^\circ\cot765\circ$ $\begin{pmatrix}\because\tan(-\theta)=-\tan\theta\\\&\cot(-\theta)=-\cot\theta\end{pmatrix}$ $=\tan\Big(\pi+\frac{\pi}{4}\Big)\cot\Big(2\pi\frac{\pi}{4}\Big)+\tan\Big(4\pi+\frac{\pi}{4}\Big)\cot\Big(4\pi-\frac{\pi}{4}\Big)$ $=\tan\frac{\pi}{4}\cot\frac{\pi}{4}+\tan\frac{\pi}{4}\times\Big(-\cot\frac{\pi}{4}\Big)$ $(\because\cot(4\pi-\theta)=-\cot\theta)$ $= 1. 1 + 1 (-1) $ $= 1 - 1$ $= 0$ $=\text{R.H.S}$ $\text{Proved}$

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 "(Each question 2 marks)" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The nth team of a sequence is given by $\text{a}_\text{n}=2\text{n}+7.$ show that it an A.P. also, find its 7th term.
→
Show that tan 3 x tan 2 x tan x = tan 3x – tan 2 x – tan x
→
One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
→
Solve the inequality 3 (2 – x) $\ge$ 2 (1 – x) for real x.
→
Let $A=\{-2,-1,0,1,2\}$ and $f: A \rightarrow Z$ be a function defined by $f(x)=x^2-2 x-3$. Find: Range of $f$ i.e., $f(A)$
→
Find the sum of the following series: 2 + 5 + 8 + ... + 182
→
Find the equation of the circle whose centre lies on the positive direction of y-axis at a distance 6 from the origin and whose radius is 4.
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sin2\text{x}}{\cos\text{x}}$
→
Solve the following linear inequations in R: $\frac{1}{\text{x}-1}\leq2$
→
If $f: R \rightarrow R$ be defined by $f(x)=x^2+1$, then find $f^{-1}\{17\}$ and $f^{-1}\{-3\}$.
→