Home
Class 10
MATHS
If 0^(@)anglethetaangle90^(@), then fi...

If `0^(@)anglethetaangle90^(@)`, then find the value of `theta` from the equation `(cos^(2)theta)/(cot^(2)theta-cos^(2)theta)=3`.

Text Solution

Verified by Experts

`(cos^(2)theta)/(cot^(2)theta-cos^(2)theta)=3`
`rArr cos^(2)theta/((cos^(2)theta)/(sin^(2)theta)-cos^(2)theta)=3rArr(cos^(2)theta)/(cos^(2)theta((1)/(sin^(2)theta)-))=3`
` rArr(1)/(1/(sin^(2)theta)-1)=3rArr(1/(1-sin^(2)theta)=3)/(sin^(2)theta)`
`rArr(sin^(2)theta)/(1-sin^(2)theta)=3rArr(sin^(2)theta)/(cos^(2)theta)=3`
`rArrtan^(2)theta=(sqrt(3))^(2)`
`rArrtantheta=sqrt(3)` (taking positive sign only)
`rArrtantheta=tan60^(@)`
`rArrtheta=60^(@)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|29 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8a|20 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11 B|10 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

Find the general value of theta from the equation costheta+cos2theta + cos3theta=0 .

Solve cosec^(2)theta-cot^(2) theta=cos theta .

find the general values of ' theta ' from the following equations costheta.cos2theta.cos3theta=1/4

Prove that cos^(2)theta("cosec"^(2)theta-cot^(2)theta)=cos^(2)theta .

Find the value of cos theta. cos 2theta. cos 2^(2)theta . cos 2^(3)theta"……." cos 2^(n-1) theta is

Find the general values of theta from the following equations: sin4theta-sin2theta=cos3theta

find the general values of ' theta ' from the following equations cos3thetacos5theta-cos7thetacos9theta=0

Find the general values of theta from the following equations: i) sin^(2)theta=3/4 ii) cos^(2)theta=1/2 iii) tan^(2)theta=1/3

If cottheta=sqrt(3) , find the value of (cos e c^2theta+cot^2theta)/(cos e c^2theta-sec^2theta)

If 4sin^(2)theta-1=0 and angle theta is less than 90^(@) , find the value of theta and hence the value of cos^(2)theta+tan^(2)theta .