Find x , if (2 x-6)= ^2 30^ - ^2 60^ - Vidyadip

Question

$
\text { Find } x \text {, if } \cos (2 x-6)=\cos ^2 30^{\circ}-\cos ^2 60^{\circ}
$

✓

Answer

$
\begin{aligned}
& \cos (2 x-6)=\cos ^2 30^{\circ}-\cos ^2 60^{\circ} \\
& \Rightarrow \cos (2 x-6)=\cos ^2\left(90^{\circ}-60^{\circ}\right)-\cos ^2 60^{\circ} \\
& \Rightarrow \cos (2 x-6)=\sin ^2 60^{\circ}-\cos ^2 60^{\circ} \\
& \Rightarrow \cos (2 x-6)=1-2 \cos ^2 60^{\circ}=1-2\left(\frac{1}{2}\right)^2=1-\frac{1}{2}=\frac{1}{2} \\
& \Rightarrow \cos (2 x-6)=\frac{1}{2} \\
& \Rightarrow \cos (2 x-6)=\cos 60^{\circ} \\
& \Rightarrow(2 x-6)=60^{\circ} \\
& \Rightarrow 2 x=66^{\circ} \\
& \Rightarrow x=33^{\circ}
\end{aligned}
$

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 "[4 marks sum]" from Trigonometric Identities→Trigonometric Identities — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

For what value of $k$ will the following quadratic equation $(k+1) x^2-4 k x+9=0$ have real and equal roots. Solve the equations.

Find the $31^{\text {st }}$ term of an $A.P$. whose $11^{\text {th }}$ term is $38$ and $6^{\text {th }}$ term is $73 .$

Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.

If $a, b, c$ and $d$ are in proportion, prove that: $ a b c d\left[\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{d^2}\right]= a ^2+ b ^2+ c ^2+ d ^2\right. $

Alex bought a game boy for $Rs. 4,784$ which included a rebate of $20\%$ and a sales tax of $15\%.$ Find the basic price of the game boy.

Pramod wants to invest Rs 35,000 in shares such that the percentage return on his investment is $8 \frac{1}{7} \%$. He invested Rs 6,000 in $6 \%$ Rs 50 shares of 'Lakme' at Rs 40, Rs 15,000 in $8 \%$ Rs 100 shares of 'Volta' at Rs 125 and the remaining in $12 \%$ shares of 'BPL'. At what rate did he buy the 'BPL' shares?

(a) Only the ruler and compass may be used in this question. All contraction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.
(i) Construct a ABC, such that AB = AC = 7 cm and BC = 5 cm.
(ii) Construct AD, the perpendicular bisector of BC.
(iii) Draw a circle with center A and radius 3 cm. Let this circle cut AD at P.
(iv) Construct another circle, to touch the circle with center A, externally at P, and pass through B and C.

The marks obtained by $19$ students of a class are given below:
$27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35$ and $28.$ Find:

Median
Lower quartile
Upper quartile
Inter-quartile range

Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.

The population of a city is $1, 25,000.$ If the annual birth rate and death rate are $5.5\%$ and $3.5\%$ respectively, calculate the population of the city after $3$ years.