Prove the following- cos sin-135 - -132 - 65-13-

cos ( sin^ 135 + ^ 132 ) = cos ( sin^ 135 ) cos ( ^ 132 ) sin ( sin^ 135 ) sin ( ^ 132 ) = √(25 9)5×3√(9 + 4) 35×2√(9 + 4) #160; = 1 ...

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

Byju's Answer

Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Prove the fol...

Question

Prove the following:
$cos ({sin}^{- 1} \frac{3}{5} + {cot}^{- 1} \frac{3}{2}) = \frac{6}{5 \sqrt{13}} .$

Open in App

Solution

$cos ({sin}^{- 1} \frac{3}{5} + {cot}^{- 1} \frac{3}{2})$
$= cos ({sin}^{- 1} \frac{3}{5}) cos ({cot}^{- 1} \frac{3}{2}) - sin ({sin}^{- 1} \frac{3}{5}) sin ({cot}^{- 1} \frac{3}{2})$
$= \frac{\sqrt{25 - 9}}{5} \times \frac{3}{\sqrt{9 + 4}} - \frac{3}{5} \times \frac{2}{\sqrt{9 + 4}}$
$= \frac{12}{5 \sqrt{13}} - \frac{6}{5 \sqrt{13}}$
$= \frac{6}{5 \sqrt{13}}$

Suggest Corrections

Similar questions

Q. Evaluate the given expression:

cos ({sin}^{- 1} \frac{3}{5} + {sin}^{- 1} \frac{5}{13})

Q. The value of

cos ({sin}^{- 1} 3 / 5)

is?

Q. Prove that

cos ({sin}^{- 1} \sqrt{\frac{9}{13}}) = sin ({tan}^{- 1} \frac{2}{3})

Q. If

I = \frac{13}{4} \div \frac{5}{6}

I I = 13 \div [(4 \div 5) \div 6]

I I I = [13 \div (4 \div 5)] \div 6

and

I V = 13 \div 4 (5 \div 6)

then, which of the following are equal?

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Join BYJU'S Learning Program

Prove the following:cos(sin−135+cot−132)=65√13.

cos(sin−135+cot−132)=cos(sin−135)cos(cot−132)−sin(sin−135)sin(cot−132)=√25−95×3√9+4−35×2√9+4 =125√13−65√13=65√13

Prove the following:
$cos ({sin}^{- 1} \frac{3}{5} + {cot}^{- 1} \frac{3}{2}) = \frac{6}{5 \sqrt{13}} .$