Prove that: 80^ - 70^ = 50^ - Vidyadip

Question

Prove that:
$\sin80^\circ-\cos70^\circ=\cos50^\circ$

✓

Answer

$\sin80^\circ-\cos70^\circ=\cos50^\circ$
$\text{LHS}=\sin80^\circ=\cos50^\circ+\cos70^\circ$
Now,
$\cos\text{C}+\cos\text{D}=2\cos\frac{\text{C+D}}{2}\cos\frac{\text{C}-\text{D}}{2}$
$\text{RHS}=\cos50^\circ+\cos70^\circ$
$=2\cos\Big(\frac{50^\circ+70^\circ}{2}\Big)\cos\Big(\frac{50^\circ-70^\circ}{2}\Big)$
$=\ 2\cos60^\circ\cos(-10^\circ)$
$=\ 2\times\frac{1}{2}\cos10^\circ$ $[\cos(-\theta)=\cos\theta]$
$=\ \cos10^\circ$
$=\ \sin80^\circ$
$=\ \text{LHS}$ $[\because\ \cos\theta=\sin(90-\theta)]$

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 Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?

Differentiate the following function with respect to x:

$\sin\text{x}\cos\text{x}$

Show that tan 3 x tan 2 x tan x = tan 3x – tan 2 x – tan x

Differentiate the following function with respect to $\text{x}$:

$\text{x}^2\text{e}^\text{x}\log\text{x}$

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

In how many ways can six persons be seated in a row?

List all the element of the following sets:
D = {x : x is a vowel in the word "EQUATION"};

Convert the following products into factorials:
1.3.5.7.9....(2n - 1)

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?