Prove that: 15^ 35^ 55^ 60^ 75^ =1 2 - Vidyadip

Question

Prove that:
$\cos15^\circ\cos35^\circ\text{cosec }55^\circ\cos60^\circ\text{cosec }75^\circ=\frac{1}{2}$

✓

Answer

$\text{L.H.S.}=\cos15^\circ\cos35^\circ\text{cosec }55^\circ\cos60^\circ\text{cosec }75^\circ$
$=\cos(90^\circ-75^\circ)\cos(90^\circ-55^\circ)\frac{1}{\sin55^\circ}\times\frac12\times\frac{1}{\sin75^\circ}$
$=\sin75^\circ\sin55^\circ\frac{1}{\sin55^\circ}\times\frac12\times\frac{1}{\sin75^\circ}$
$=\frac{1}{2}$
$=\text{R.H.S.}$

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 "5 Marks Questions" from Trigonometric Ratios of Complementary Angles→Trigonometric Ratios of Complementary Angles — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Prove that both the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are real but they are equal only when a = b = c.

Let there be an A.P. with first term ' $a$ ', common difference ' $d$ '. If $a_n$ denotes in $n ^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find. n and a , if $a _{ n }=4, d=2$ and $S _{ n }=-14$.

A bucket has top and bottom diameter of 40cm and 20cm respectively. Find the volume of the bucket if its depth is 12cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per $dm^2$. $(\text{use}\ \pi=3.14)$

Calculate the median from the following frequency distribution:

Class	5-10	10-15	15-20	20-25	20-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
4x - 3y + 4 = 0, 4x + 3y - 20 = 0

A man walks a certain distance with certain speed. If he walks $\frac{1}{2}$km an hour faster, he takes 1 hour less. But, if he walks 1km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Solve the following quadratic equation:
$3\Big(\frac{\text{3x}-1}{\text{2x}+3}\Big)-2\Big(\frac{\text{2x}+3}{\text{3x}-1}\Big)=5$ $\text{x}\neq\frac{1}{3},\ \frac{-3}{2}$

A train travels 360km at a uniform speed. If the speed had been 5km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Prove that $\frac{1}{(sec\theta-\tan\theta)}-\frac{1}{\cos\theta}=\frac{1}{\cos\theta}-\frac{1}{(\sec\theta+\tan\theta)}.$

The barrel of a fountain pen, cylindrical in shape, is 7cm long and 5mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?