CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Trigonometric Ratios for Sum of Two Angles

Prove that: i...

Question

Prove that: $(i i)$ $\frac{1}{sin (x - a) cos (x - b)} = \frac{cot (x - a) + tan (x - b)}{cos (a - b)}$

Open in App

Solution

To Prove : $\frac{1}{sin (x - a) cos (x - b)} = \frac{cot (x - a) + tan (x - b)}{cos (a - b)}$
Taking R.H.S.
$\frac{cot (x - a) + tan (x - b)}{cos (a - b)}$
$\frac{\frac{cos (x - a)}{sin (x - a)} + \frac{sin (x - b)}{cos (x - b)}}{cos (a - b)}$
$= \frac{cos (x - b) cos (x - a) + sin (x - b) sin (x - a)}{sin (x - a) cos (x - b) cos (a - b)}$
$[∵ cos A cos B + sin A sin B = cos (A - B)]$
$= \frac{cos (x - b - x + a)}{sin (x - a) cos (x - b) cos (a - b)}$
$= \frac{1}{sin (x - a) cos (x - b)}$
Hence proved.

Suggest Corrections

thumbs-up

1

Similar questions

Q. Prove that:

(i)

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1

Prove that:

(i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

(ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

Prove that:
(i) $\frac{1}{s i n (x - a) s i n (x - b)} = \frac{c o t (x - a) - c o t (x - b)}{s i n (a - b)}$
(ii) $\frac{1}{s i n (x - a) c o s (x - b)} = \frac{c o t (x - a) + t a n (x - b)}{c o s (a - b)}$

Q. Prove that:

(i)

\frac{1}{\sin (x - a) \sin (x - b)} = \frac{\cot (x - a) - \cot (x - b)}{\sin (a - b)}

\frac{1}{\sin (x - a) \cos (x - b)} = \frac{\cot (x - a) + \tan (x - b)}{\cos (a - b)}

\frac{1}{\cos (x - a) \cos (a - b)} = \frac{\tan (x - b) - \tan (x - a)}{\sin (a - b)}

Q. Prove that:

(i)

\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c

{(a^{- 1} + b^{- 1})}^{- 1} = \frac{a b}{a + b}

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Trigonometric Ratios for Sum of Two Angles

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon