Home
Class 12
MATHS
If 3tanthetatanphi=1 , then prove that 2...

If `3tanthetatanphi=1` , then prove that `2cos(theta+phi) = cos(theta-phi)`

Text Solution

Verified by Experts

Given, `3 tan theta tan varphi=1` or not `cot theta cot psi=3`
or `(cos theta cos varphi)/(Sin theta sin varphi)=(3)/(1)`
By componendo and dividendo, we get
`(cos theta cos varphi +sin theta sin varphi )/(cos theta cos varphi -sin thetasin varphi)=(3+1)/(3-1)`
or `(cos(theta-varphi))/(cos (theta+varphi))=2`
or `2cos(theta+varphi)=cos(theta-varphi)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.1|11 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.2|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

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

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that cos (pi + theta) = - cos theta

If theta + phi = alpha and tan theta = k tan phi , then prove that sin (theta - phi) = (k - 1)/(k + 1) sin alpha .

If theta + phi =alpha and tan theta = k tan phi , then prove that sin(theta - phi) =(k-1)/(k+1) sin alpha .

If tan (phi /2)= sqrt((1+a)/(1-a)) tan"" theta/2," then prove that cos "phi=(cos theta-a)/(1-a cos theta)

Prove that: cos^2 theta (1 + tan^2 theta) = 1

Prove that: (sin2theta)/(1-cos2theta)=cottheta

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

If sintheta(1+sin^(2)theta)=cos^(2)theta , then prove that cos^(6)theta-4cos^(2)theta+8cos^(2)theta=4

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0