Question

Prove that
( Sin 7-sin 5)÷cos 7+cos 5=tan

Answer 1

RS agarwal pg 115 class 10

Answer 2

Answer:

L.H.S = R.H.S

Step-by-step explanation:

In this question

We have been given that

$\frac{sin 7 - sin 5}{cos 7 - cos 5}$ = tan 1

Let, L.H.S

$\frac{sin 7 - sin 5}{cos 7 - cos 5}$

${cos 7 - cos 5}$ firstly solve this equation

Using this formula

$cos x - cos y$ = $2cos\frac{x + y}{2} cos\frac{x - y}{2}$

Here, x = 7 and y = 5

Then, $2cos\frac{7 + 5}{2} cos\frac{7 - 5}{2}$

$2cos\frac{12}{2} cos\frac{2}{2}$

$2cos 6 cos 1$

${sin 7 - sin 5}$ solve this equation

$sin x - sin y$ = $2cos\frac{x + y}{2} sin\frac{x - y}{2}$

Here, x = 7 and y = 5

$2cos\frac{7 + 5}{2} sin\frac{7 - 5}{2}$

$2cos\frac{12}{2} sin\frac{2}{2}$

$2cos 6 sin 1$

$\frac{2cos 6 sin 1}{2cos 6 cos 1}$

$\frac{sin 1}{cos 1}$

$tan 1$

R.H.S