Home
Class 12
MATHS
Show that cos^2theta+cos^2theta(alpha+th...

Show that `cos^2theta+cos^2theta(alpha+theta)-2cosalphacostheta"cos"(alpha+theta)` is independent of `thetadot`

Text Solution

Verified by Experts

`cos^(2)theta+cos^(2)(alpha+theta)-2cosalpha cos theta cos (alpha+theta)`
`=cos^(2)theta+cos(alpha+theta)[cos(alpha+theta)-2cos alpha cos theta]`
`=cos^(2)theta+cos(alpha+theta)`
`[cos alpha cos theta-sin alpha sin theta-2cos alpha cos theta]`
`cos^(2)theta-cos(alpha+theta)(cos alpha cos theta+sin alpha sin theta)`
`=cos^(@)theta-cos(alpha+beta)cos(alpha-theta)`
`=cos^(2)theta-[cos^(2)alpha-sin^(2)theta]=cos^(2)theta+sin^(2)theta-cos^(2)alpha`
`=1-cos^(2)alpha`, which is independent of `theta`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Show that cos^2theta+cos^2(alpha+theta)-2cosalphacostheta"cos"(alpha+theta) is independent of thetadot

Prove that : 2 sin^2 theta + 4 cos (theta + alpha) sin alpha sin theta + cos 2 (alpha + theta) is independent of theta.

Solve: cos2theta=cos^(2)theta

The expression nsin^(2) theta + 2 n cos( theta + alpha ) sin alpha sin theta + cos2(alpha + theta ) is independent of theta , the value of n is

Prove that cos 4theta–cos 4alpha = 8(cos theta-cos alpha)(cos theta+ cos alpha )(cos theta -sin alpha)(cos theta+sin alpha)

Prove that: cos^2theta=cos^2alpha then theta=npi+-alpha,n in Z

Solve the equation : cos^2 theta = cos^2 alpha

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

Solve cos theta+cos 2theta+cos 3theta=0 .

Prove (cos 3theta+ 2 cos 5theta+ cos 7theta)/( cos theta+ 2 cos 3theta+ cos 5theta)= cos 2theta- sin 2theta tan 3theta .