hamburger menu
All Coursesall course arrow
adda247
reward-icon
adda247
    Home
    arrow
    Quantitative Aptitude
    arrow
    Trigonometry
    arrow
    If x+1/x=2 cos⁡θ,  then what is the value of x2+1x2x^2+\frac{1}{x^2}x2+x21​​ ?
    Question

    If x+1/x=2 cos⁡θ,  then what is the value of x2+1x2x^2+\frac{1}{x^2}​ ?

    A.

    sin⁡2θ

    B.

    2 cos⁡2θ

    C.

    2 sin⁡2θ

    D.

    cos⁡2θ

    Correct option is B

    Given: ​
    x+1x=2cos⁡θ x+\frac{1}{x}=2 cos⁡θ​, 
    To, find value of x2+1x2x^2+\frac{1}{x^2} 
    Formula Used: ​
    ​(a+b)2=a2+b2+2ab(a +b)^2 = a^2 + b^2 + 2ab    
    ​cos⁡2θ=2cos⁡2θ−1\cos 2 \theta = 2\cos^2 \theta -1​​
    Solution:  
    ​x+1x=2cos⁡θ x+\frac{1}{x}=2 cos⁡θ​,  
    squaring both side;
    we get :
    ​(x+1x)2=(2cos⁡θ)2 x2+1x2+2=4cos⁡2θ x2+1x2=4cos⁡2θ−2 x2+1x2=2(2cos⁡2θ−1) x2+1x2=2cos⁡2θ\left( x+\frac{1}{x} \right)^2 = (2 \cos \theta)^2 \\ \ \\x^2 + \frac{1}{x^2 }+2 = 4 \cos^2 \theta \\ \ \\x^2 + \frac{1}{x^2 } = 4 \cos^2 \theta -2 \\ \ \\x^2 + \frac{1}{x^2 } = 2(2\cos^2 \theta - 1) \\ \ \\x^2 + \frac{1}{x^2 } = 2\cos 2 \theta ​​​

    Free Tests

    Free
    Must Attempt

    CBT-1 Full Mock Test 1

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English
    Free
    Must Attempt

    RRB NTPC Graduate Level PYP (Held on 5 Jun 2025 S1)

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English
    Free
    Must Attempt

    RRB NTPC UG Level PYP (Held on 7 Aug 2025 S1)

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English

    Similar Questions

    test-prime-package

    Access ‘RRB NTPC’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    BUY NOW
    students-icon
    368k+ students have already unlocked exclusive benefits with Test Prime!

    Suggested Test Series

    RRB NTPC Graduate (CBT 1 + CBT 2 + Psycho) 2025-26 Mock Test
    RRB NTPC Graduate (CBT 1 + CBT 2 + Psycho) 2025-26 Mock Test
    795 Tests + 2 Free Tests
    button-right
    RRB NTPC Under Graduate (CBT 1 + CBT 2) 2025-26 Mock Test
    RRB NTPC Under Graduate (CBT 1 + CBT 2) 2025-26 Mock Test
    968 Tests + 1 Free Tests
    button-right
    RRB Group D 2025-26 Mock Test
    RRB Group D 2025-26 Mock Test
    883 Tests + 3 Free Tests
    button-right
    RRB Technician Grade III 2025 Mock Test
    RRB Technician Grade III 2025 Mock Test
    291 Tests + 2 Free Tests
    button-right
    RRB JE (CBT 1 & CBT 2) 2026 Mock Test
    RRB JE (CBT 1 & CBT 2) 2026 Mock Test
    474 Tests + 2 Free Tests
    button-right
    test-prime-package

    Access ‘RRB NTPC’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    BUY NOW
    students-icon
    368k+ students have already unlocked exclusive benefits with Test Prime!

    Suggested Test Series

    RRB NTPC Graduate (CBT 1 + CBT 2 + Psycho) 2025-26 Mock Test
    RRB NTPC Graduate (CBT 1 + CBT 2 + Psycho) 2025-26 Mock Test
    795 Tests + 2 Free Tests
    button-right
    RRB NTPC Under Graduate (CBT 1 + CBT 2) 2025-26 Mock Test
    RRB NTPC Under Graduate (CBT 1 + CBT 2) 2025-26 Mock Test
    968 Tests + 1 Free Tests
    button-right
    RRB Group D 2025-26 Mock Test
    RRB Group D 2025-26 Mock Test
    883 Tests + 3 Free Tests
    button-right
    RRB Technician Grade III 2025 Mock Test
    RRB Technician Grade III 2025 Mock Test
    291 Tests + 2 Free Tests
    button-right
    RRB JE (CBT 1 & CBT 2) 2026 Mock Test
    RRB JE (CBT 1 & CBT 2) 2026 Mock Test
    474 Tests + 2 Free Tests
    button-right
    Our Plans
    Monthsup-arrow
    BUY NOW