Home
Class 11
MATHS
Solve (sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(...

Solve `(sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(5)))/(cosx)=8,x in (0,pi/2)`

Text Solution

Verified by Experts

We have `(sqrt(5)-1)/4xx1/(sin x)+sqrt(10+2sqrt(5))/4xx1/(cos x)=2`
`rArr ((sqrt(5)-1))/4 cos x + sqrt(10+2sqrt(5))/4sin x=2 sin x. cos x`
`rArr sin (x+pi/10)=sin 2x or sin (x+pi/10)= sin (pi-2x)`
`rArr x+pi/10=2x" "or x+pi/10=pi-2x`
`rArr x=pi/10" "or 3x=pi-pi/10=(9pi)/10`
`rArr x=pi/10" "or x=(3pi)/10`
Promotional Banner

Similar Questions

Explore conceptually related problems

cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), x in (0,(pi)/(4))

Solve ((8+sqrt5)/(8-sqrt5))+((8-sqrt5)/(8+sqrt5))

Solve: sqrt(5)x^(2) + x + sqrt(5) = 0

If y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))), x in ((pi)/(2), pi) , then (dy)/(dx) at x=(5pi)/(6) is :

int_0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx

Solve for x:x^(2)-(sqrt(5)+1)x+sqrt(5)=0

Solve the equation sinx +sqrt(3) cosx=sqrt(2)

Solve: (sinx+cosx)/(sinx-cosx)=(sqrt(3)+1)/(sqrt(3)-1)