Home
Class 12
MATHS
If cos theta - sin theta = (1)/(5), wher...

If `cos theta - sin theta = (1)/(5)`, where `0 lt theta lt (pi)/(4)`, then

Text Solution

Verified by Experts

The correct Answer is:
`a to q; b to r; c to s; d to p`

`cos theta - sin theta = (1)/(5)`, where `0 lt theta lt (pi)/(2)" "` ...(i)
Squaring both sides of Eq. (i), we get
`1-sin2theta = (1)/(25)`
`or " " sin 2theta = (24)/(25)`
`or " " cos 2theta = (7)/(25)`
Also, `(cos theta + sin theta)^(2) = (cos theta - sin theta )^(2) + 4 cos theta sin theta `
`= (1)/(25) + 2 sin 2theta = (1)/(25) + (48)/(25) = (49)/(25)`
`rArr cos theta + sin theta = (7)/(5)" "`...(ii)
or `" "((cos theta + sin theta))/(2) = (7)/(10)`
Also solving Eqs. (i) and (ii), we geet `cos theta = 4//5`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Numerical)|38 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise JEE Main Previous Year|5 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 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

If x = sum_(n = 0)^(infty) cos ^(2n) theta, " "y = sum_(n = 0)^(infty) sin^(2n) theta and z = sum_(n = 0)^(infty) cos^(2n) theta sin^(2n)theta, 0 lt theta lt (pi)/(2) , then show that xyz = x + y + z [ Hint : use the formula 1 + x + x^(2) + x^(3) +... =(1)/(1 - x) , where |x| lt 1 ]

Solve 2cos^2theta+sinthetalt=2, where pi/2lt=thetalt=(3pi)/2dot

Knowledge Check

  • Let A={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin theta , 1 )]:} ,"where" 0 letheta le 2pi , Then

    A
    `Det(A) =0`
    B
    ` Det(A) in (-2, infty ) `
    C
    `Det (A) in (2,0) `
    D
    `Det(A) in [2,4]`
  • IF sin theta = sin 15^@ + sin 45^@ , where 0^@ lt theta lt 90 ^@ , then theta is equal to

    A
    `45^@`
    B
    `54^@`
    C
    `60^@`
    D
    `75^@`
  • IF 8 cos 2 theta + 8 sec 2 theta = 65 , 0 lt (pi)/(2) , then the value of 4 cos 4 theta is equal to

    A
    `(-33)/(8)`
    B
    `(-31)/(8)`
    C
    `(-31)/(32)`
    D
    `(-33)/(32)`
  • Similar Questions

    Explore conceptually related problems

    Solve tan theta tan 4theta=1 for - lt theta lt pi .

    Choose the odd one out (1) x = a cos theta , y = a sin theta (2) theta (3) 0 ge theta ge 2 pi (4) ( a cos theta , b sin theta)

    If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)

    Prove the following: (sin theta - cos theta + 1 )/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)

    IF tan ( pi cos theta) = cot ( pi sin theta ) then cos ( theta - (pi)/(4)) is equal to