Answer :

Given 4m = cotx (1+ sinx) and 4n = cotx (1 – sinx)


Multiplying both equations, we get


16mn = cot2x (1 – sin2x)


We know that 1 – sin2x = cos2x


16mn = cot2x cos2x


… (1)


Squaring the given equations and then subtracting,


16m2 = cot2x (1+ sinx)2 and 16n2 = cot2x (1 – sinx)2


16m2 – 16n2 = cot2x (4 sinx)



Squaring both sides,



… (2)


From (1) and (2),


(m2 – n2) = mn


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

True and False<brMathematics - Exemplar

Find the values oRD Sharma - Mathematics

Prove that :
<
RD Sharma - Mathematics

The value of cos<Mathematics - Exemplar

The value of sin Mathematics - Exemplar

cos 2θ cos 2<spanMathematics - Exemplar

The value of <spaMathematics - Exemplar

If <span lang="ENMathematics - Exemplar

If <span lang="ENMathematics - Exemplar

Fill in the blankMathematics - Exemplar