Home
Class 12
MATHS
If m^2+m^('2)+2mn'cos theta =1 n^2+n^(...

If `m^2+m^('2)+2mn'cos theta =1`
`n^2+n^('2)+2"nn"' cos theta=1 and mn +m'n'+(mn'+m'n)cos theta=0` then show that `m^2+n^2=m^('2) +n^('2) =cosec^2 theta`.

Text Solution

Verified by Experts

The correct Answer is:
Hence , we have , `m^2+n^2=m^('2)+n^('2) =cosec^2theta`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise EXERCISE 2|94 Videos
  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|1 Videos
  • TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos
  • VECTOR

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION|18 Videos

Similar Questions

Explore conceptually related problems

If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3) , then prove that m^(2)n^(2)(m^(2)+n^(2))=1.

If " cosec"theta-sin theta=m and sec theta-cos theta=n , then prove that (m^(2)n)^((2)/(3))+(mn^(2))^((2)/(3))=1.

If x = sec theta - cos theta, y = sec^n theta - cos^n theta , then show that (x^2 + 4) (dy/dx)^2 = n^2 (y^2 + 4)

If m= sin ^(2) theta + cos ^(4)theta, then-

If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = sin theta (1 + cos2 theta) + sin 2 theta(1 + cos theta), "show that" u^(2) + v^(2) = 4(1 + cos theta) (1 + cos 2theta).

If (m+2) sin theta+(2m-1) cos theta=(2m+1) , then show that tan theta= =(4)/(3)or (2m)/(m^(2)-1) .

If c cos^(3)theta+3c cos theta sin^(2)theta=m and c sin^(3)theta+3c cos^(2)theta sin theta=n , then prove that (m+n)^((2)/(3))+(m-n)^((2)/(3))=2c^((2)/(3)).

If tanA+sinA=m and tanA-sinA=n , then prove that m^(2)-n^(2)=4sqrt(mn) .