Evaluate the following: 2 ^260^ +3 ^245^ -3 ^230^ +2 ^290^ - Vidyadip

Question

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

✓

Answer

On substituting values of various T-ratious, we get:
$2\cos^260^\circ+3\sin^245^\circ-3\sin^230^\circ+2\cos^290^\circ$
$=2\times\Big(\frac12\Big)^2+3\times\Big(\frac{1}{\sqrt{2}}\Big)^2-3\times\Big(\frac12\Big)^2+2\times(0)^2$
$=2\times\frac14+3\times\frac12-3\times\frac14+0$
$=\Big(\frac12+\frac32-\frac34\Big)=\Big(\frac{2+6-3}{4}\Big)=\frac54$

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 of Some Particular Angles→Trigonometric Ratios of Some Particular Angles — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

If the distance between the points $(3, 0)$ and $(0, y)$ is $5$ units and $y$ is positive. then what is the value of $y$?

In $\triangle P Q R, M$ is the midpoint of side $Q R$. If $P Q=11, P R=17$ and $Q R=12$, then find $P M$.

If A + B = 90° and $\tan\text{A}=\frac{3}{4},$ what is cot B?

If $\tan\text{A}=\frac{3}{4}$ and A + B = 90°, then what is the value of cot B?

Write one example of finite and infinite A.P. each.

Prove the following trigonometric identities.
$\frac{1+\cos\theta-\sin^2\theta}{\sin\theta(1+\cos\theta)}=\cot\theta$

Use Euclid's division algorithm to find the HCF of:
196 and 38220

‘M/s. Real Paint’ sold 2 tins of lustre paint and taxable value of each tin is Rs. 2800. If the rate of GST is 28%, then find the amount of CGST and SGST charged in the tax invoice.

Three cubes of iron whose edges are $6\ cm, 8\ cm$ and $10\ cm$, respectively are melted and formed into a single cube. Find the edge of the new cube formed.

Find the sum of the following APs:
-37, -33, -29, .... to 12 terms.