Prove that: 225^ 405^ + 765^ 675^ =0 - Vidyadip

Question

Prove that: $\tan225^\circ\cot405^\circ+\tan765^\circ\cot675^\circ=0$

✓

Answer

$\text{L.H.S}=\tan225^\circ\cot405^\circ+\tan765^\circ\cot675^\circ$ $=\tan\Big(\pi+\frac{\pi}{4}\Big)\cot\Big(2\pi+\frac{\pi}{4}\Big)+\tan\Big(4\pi+\frac{\pi}{4}\Big)\cot\Big(4\pi-\frac{\pi}{4}\Big)$ $=\tan\frac{\pi}{4}.\cot\frac{\pi}{4}+\tan\frac{\pi}{4}\times\Big(-\cot\frac{\pi}{4}\Big)$ $\Big(\because\cot\Big(4\pi-\frac{\pi}{4}\Big)=-\cot\frac{\pi}{4}\Big)$ $= 1.1 + 1. (-1)$ $= 0$ $\text{= R.H.S}$ $\text{Proved}$

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 3 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

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always $10 m$ and the distance between the flag posts is $8 m$. Find the equation of the path traced by the man.

Solve the following equations: $\sec\text{x}\cos5\text{x}+1=0,0<\text{x}<\frac{\pi}{2}$

Solve the inequality graphically in a two-dimensional plane: x – y $\leq$ 2

$\text{x}^6+\text{x}^4+\text{x}^2+1,$ when $\text{x}=\frac{1+\text{i}}{\sqrt{2}}.$

Differentiate the following function with respect to x:$\text{x}^{-3}(5+\text{3x})$

Solve:25 + 22 + 19 + 16 + ... + x = 115

Point R(h, k) divides a line segment between the axis in the ratio 1 : 2. Find equation of the line.

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A′, B′ , A′ $\cap$ B′, A $\cup$B and hence show that (A $\cup$B)′ = A′ $\cap$B′

Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}. Verify the following identities:
$\text{A}\cap(\text{B}-\text{C})=(\text{A}\cap\text{B})-(\text{A}\cap\text{C})$

Evaluate the following:$\sum_\limits{\text{n}=2}^{10}(4^\text{n})$