Home
Class 11
MATHS
Prove: sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4...

Prove: `sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4`

Text Solution

Verified by Experts

Let `cot^-1 3 = theta`.
Then, `cot theta = 3`
`=>costheta/sintheta = 3 =>cos^2theta/sin^2theta = 9`
`=>(1-sin^2theta)/sin^2theta = 9 =>sintheta = 1/sqrt10`
`=> theta = sin^-1(1/sqrt10)`
`:. L.H.S. = sin^-1(1/sqrt5) +sin^-1(1/sqrt10)`
We know, `sin^-1x+sin^-1y = sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2))`
So, our expression becomes,
...
Promotional Banner

Similar Questions

Explore conceptually related problems

sin ^(-1) (1)/(sqrt(5))+cot ^(-1) 3=

Prove: cot^(-1)(1/2)-1/2cot^(-1)(4/3)=pi/4

Value of "sin"^(-1)(1)/(sqrt(5))+cot^(-1)3 '' is

sin ^(-1) "" (1)/(sqrt(5))+cot ^(-1) 3= (pi)/(4)

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Prove that: i) sin^(-1)(1/sqrt(5))+sin^(-1)(2/sqrt(5))=pi/2