Evaluate the following: ( 72^ + 18^ )( 72^ - 18^ ) - Vidyadip

Question

Evaluate the following:
$(\sin72^\circ+\cos18^\circ)(\sin72^\circ-\cos18^\circ)$

✓

Answer

We have to find: $(\sin72^\circ+\cos18^\circ)(\sin72^\circ-\cos18^\circ)$$$Since $\sin(90^\circ-\theta)=\cos\theta$
So, $(\sin72^\circ+\cos18^\circ)(\sin72^\circ-\cos18^\circ)=(\sin72^\circ)^2-(\cos18^\circ)^2$ $=[\sin(90^\circ-18^\circ)]^2-(\cos18^\circ)^2$ $=(\cos18^\circ)^2-(\cos18^\circ)^2$ $=\cos^218^\circ-\cos^218^\circ$ $=0$So value of $(\sin72^\circ+\cos18^\circ)(\sin72^\circ-\cos18^\circ)\text{ is }0$

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 Ratios→Trigonometric Ratios — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ in dividing $f(x)$ by $g(x)$ in the following:
$f(x) = x^3 - 6x^2 + 11x - 6, g(x) = x^2 + x + 1$

Which of the following are quadratic equations?
$\text{x}+\frac{1}{\text{x}}=1$

The first term a and common difference d are given. Find first four terms of A.P :

$a=200, d=7$

Prove the following.
$\frac{1}{1-\sin \theta}+\frac{1}{1+\sin \theta}=2 \sec ^2 \theta$

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is
a multiple of 5 ?

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\cos\theta=\frac{7}{25}$

Prove the following trigonometric identities.
$(\sec^2\theta-1)(\text{cosec}^2\theta-1)=1$

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Find the value of $\left|\begin{array}{cc}5 & 2 \\ 0 & -1\end{array}\right|$

How many cubes of 10cm edge can be put in a cubical box of m edge?