Evaluate the following: ( 27^ 63^ )^2- ( 63^ 27^ )^2 - Vidyadip

Question

Evaluate the following:
$\Big(\frac{\sin27^\circ}{\cos63^\circ}\Big)^2-\Big(\frac{\cos63^\circ}{\sin27^\circ}\Big)^2$

✓

Answer

We have to find: $\Big(\frac{\sin27^\circ}{\cos63^\circ}\Big)^2-\Big(\frac{\cos63^\circ}{\sin27^\circ}\Big)^2$$$
Since $\sin(90^\circ-\theta)=\cos\theta$ and $\cos(90^\circ-\theta)=\sin\theta$
So, $\Big(\frac{\sin27^\circ}{\cos63^\circ}\Big)^2-\Big(\frac{\cos63^\circ}{\sin27^\circ}\Big)^2=\bigg[\frac{\sin(90^\circ-63^\circ)}{\cos63^\circ}\bigg]^2-\bigg[\frac{\cos(90^\circ-27^\circ)}{\sin27^\circ}\bigg]^2$
$=\Big(\frac{\cos63^\circ}{\cos63^\circ}\Big)^2-\Big(\frac{\sin27^\circ}{\sin27^\circ}\Big)^2$
$= 1 - 1$
$= 0$
So value of $\Big(\frac{\sin27^\circ}{\cos63^\circ}\Big)^2-\Big(\frac{\cos63^\circ}{\sin27^\circ}\Big)^2\text{ is }0$

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→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Which of the following are quadratic equations?
$x(x + 1) + 8 = (x + 2)(x - 2)$

Has the rational number $\frac{441}{2^2\times5^7\times7^2}$ terminating or a non terminating decimal representation?

On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equations are consistent, or inconsistent: 3x + 2y = 5, 2x − 3y = 7.

Euclid's algorithm, find the HCF of 240 and 228.

Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?

How many terms of $ A.P. 27,24,21, \ldots$. should be taken so that their sum is zero $( 0 )$?

Very-Short and Short-Answer Questions:
If $\frac{\text{x}}{4}+\frac{\text{y}}{\text{3}}=\frac{5}{\text{12}}$ and $\frac{\text{x}}{\text{2}}+\text{y}=1$ then find the value of (x + y).

Find the value of $' k\ '$ so that the quadratic equation $3 x^2-5 x-2 k=0$ has real and equal roots.

Answer the following and justify:
If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?

Evaluate the following:
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$