Home
Class 11
MATHS
Find the most general value of theta sa...

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

A

`theta= 2npi+(7pi)/(4)`.

B

`theta= npi+(7pi)/(4)`.

C

`theta= 2npi+(pi)/(4)`.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The given equations are
`" " tantheta=-1 " "...(i)`
and `" "costheta=(1)/(sqrt(2))" "...(ii)` ltBrgt From Eq. (i), `" " tantheta=-tan""(pi)/(4)`
` rArr" "tantheta=tan(2pi-(pi)/(4))rArrtantheta=tan""(7pi)/(4)`
` rArr" "tantheta=tan(2pi-(pi)/(4))rArrtantheta=tan""(7pi)/(4)`
From Eq. (ii), `" "costheta=(1)/(sqrt (2))rArrcostheta=cos""(pi)/(4)`
`rArr" "costheta=cos(2pi-(pi)/( 4))rArrcostheta=cos""(7pi)/(4)`
`therefore" "theta=(7pi)/(4)`
Hence, the most general value of `theta` i.e., `theta= 2npi+(7pi)/(4)`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|31 Videos

  • STRAIGHT LINES

    NCERT EXEMPLAR|Exercise MATCHING THE COLUMN|3 Videos

Similar Questions

Explore conceptually related problems

Find the mos general values of theta satisfying the equation :sin theta=-1

Find the general values of theta which satisfies the equation tan theta =-1 and cos theta =(1)/(sqrt(2))

The most general value of theta satisfying the equations sin theta=(1)/(sqrt(2)) and cos theta=-(1)/(sqrt(2)) is

The most general value of theta satisfying both the equations sin theta=(1)/(2):tan theta=(1)/(sqrt(3)) is

Find the most general value of theta which satisfies the equation sin theta =-(1)/(2) and tan theta =(1)/(sqrt(3))

What are the most general values of theta which satisfy the equations tantheta = -1

Most general value of theta satisfying equation tan^(2)theta+sec2 theta=1 is

The most general values of theta satisfying the two equations cos theta=-(1)/(sqrt(2)),tan theta=1 is

The most general values of theta satisfying the two equations cos theta=-(1)/(sqrt(2)),tan theta=1 is