Home
Class 12
MATHS
Prove that sec((3pi)/2-theta)sec(theta-(...

Prove that `sec((3pi)/2-theta)sec(theta-(5pi)/2)+tan((5pi)/2+theta)tan(theta-(3pi)/2)=-1`

Text Solution

Verified by Experts

`sec((3pi)/2-theta)sec(theta-(5pi)/2)+tan((5pi)/2+0)tan(theta-(3pi)/2)`
`=-cosecthetacosectheta+cotthetacot theta`
`=-(cosec^2theta-cot^2theta)=-1`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|57 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.5|16 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Prove that tan ((pi)/(4) + theta)- tan ((pi)/(4) - theta) = 2 tan 2 theta .

Prove that (sec 8theta-1)/(sec 4 theta -1) = (tan 8theta)/(tan 2theta)

Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=0

Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/(tan theta)

Prove that (sec theta+cos theta) (sec theta-cos theta)=tan^(2) theta+sin^(2) theta

Prove that tan ((pi)/(4) + theta) tan ((3pi)/(4) + theta) = -1

Prove that |(sec^(2)theta,tan^(2)theta,1),(tan^(2)theta,sec^(2)theta,-1),(38,38,2)|=0.

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that following identities sec^(4)theta(1-sin^(4)theta)-2tan^(2)theta=1