Home
Class 11
MATHS
Find the general value of theta from the...

Find the general value of `theta` from the equation `tantheta-sqrt(2)sectheta=1`.

Text Solution

Verified by Experts

`tantheta-sqrt(2)sectheta=1`
`=(sintheta)/(costheta)-sqrt(2)/(costheta)=1`
`rArr sintheta-sqrt(2)=costheta`
`rArr sintheta-costheta=sqrt(2)`
Squaring both sides we get
`sin^(2)theta+cos^(2)theta-2sinthetacostheta=2`
`1-sin2theta=2`
`rArr sin2theta=-sinpi/2`
`sin2theta=-sin(-pi/2)`
`rArr 2theta=npi+(-1)^(n).(-pi/2)`
`rArr theta=(npi)/2-(-1)^(n).pi/4`. Ans.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3A|11 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3B|22 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

Similar Questions

Explore conceptually related problems

Find the general value of theta from the equation tantheta+tan2theta+tan3theta=tantheta*tan2theta*tan3theta.

Find the general value of theta from the equation tantheta+tan3theta=2tan2theta .

Find the general value of theta from the equation sintheta+costheta=sqrt(2)cosA.

Find the general values of theta from the following equations: i) sintheta=-sqrt(3)/(2) ii) sectheta=-sqrt(2) iii) cottheta=-1/sqrt(3) , iv) "cosec"theta=-2

The general value of theta in the equation 2sqrt(3)costheta=tantheta is

Find the geneal values of theta from the following equations: i) sintheta=sqrt(3)/2 , ii) costheta=1/sqrt(2) , iii) tantheta=sqrt(3) , iv) sectheta=2/sqrt(3) , v) cottheta=1/sqrt(3) , vi) "cosec"theta=sqrt(2)

Find the general value of theta from the following equations :2(cos^(2)theta-sin^(2)theta)=1

Find the most general value of theta satisfyingn the equation tantheta=-1 and costheta=(1 )/(sqrt(2)) .