1800-150-456-789
FlagBACK
Flag Trigonometry> Prove that {1/(sec^2 a-cos^2 a) + 1/(cose...
question mark

Prove that
{1/(sec^2 a-cos^2 a) + 1/(cosec^2 a-sin^ a)}*cos^2 a sin^2 a=(1-cos^2 a sin^2 a)/(2+cos^2 a sin^2 a)

Bahirithi , 6 Years ago
Grade 12
anser 1 Answers
Aarushi Ahlawat

Last Activity: 6 Years ago

 
 
First convert all the terms to sin and cos terms and then use identity to replace sin^2a+cos^a with 1. Here are the steps
LHS=\left [ \frac{1}{sec^{2}(a)-cos^{2}(a)}+\frac{1}{cosec^{2}(a)-sin^{2}(a)} \right ]cos^{2}(a)sin^{2}(a)
 
=\left [ \frac{cos^{2}(a)}{1-cos^{4}(a)}+\frac{sin^{2}(a)}{1-sin^{4}(a)} \right ]cos^{2}(a)sin^{2}(a)
=\left [ \frac{cos^{2}(a)}{(1-cos^{2}(a))(1+cos^{2}(a))}+\frac{sin^{2}(a)}{(1-sin^{2}(a))(1+sin^{2}(a))} \right ]cos^{2}(a)sin^{2}(a)
=\left [ \frac{cos^{2}(a)}{sin^{2}(a)(1+cos^{2}(a))}+\frac{sin^{2}(a)}{cos^{2}(a)(1+sin^{2}(a))} \right ]cos^{2}(a)sin^{2}(a)
=\left [ \frac{cos^{2}(a)cos^{2}(a)(1+sin^{2}(a))+sin^{2}(a)sin^{2}(a)(1+cos^{2}(a))}{sin^{2}(a)(1+cos^{2}(a))cos^{2}(a)(1+sin^{2}(a))} \right ]cos^{2}(a)sin^{2}(a)
=\frac{cos^{4}(a)(1+sin^{2}(a))+sin^{4}(a)(1+cos^{2}(a))}{(1+cos^{2}(a))(1+sin^{2}(a))}
=\frac{cos^{4}(a)+cos^{4}(a)sin^{2}(a)+sin^{4}(a)+sin^{4}(a)cos^{2}(a))}{(1+cos^{2}(a)+sin^{2}(a)+cos^{2}(a)sin^{2}(a))}
=\frac{cos^{4}(a)+sin^{4}(a)+cos^{2}(a)sin^{2}(a)(sin^{2}(a)+cos^{2}(a))} {(1+1+cos^{2}(a)sin^{2}(a))}
=\frac{cos^{4}(a)+sin^{4}(a)+cos^{2}(a)sin^{2}(a)} {(2+cos^{2}(a)sin^{2}(a))}
=\frac{cos^{4}(a)+sin^{4}(a)+2cos^{2}(a)sin^{2}(a)-cos^{2}(a)sin^{2}(a)} {(2+cos^{2}(a)sin^{2}(a))}
=\frac{(cos^{2}(a)+sin^{2}(a))^{2}-cos^{2}(a)sin^{2}(a)} {(2+cos^{2}(a)sin^{2}(a))}
=\frac{1-cos^{2}(a)sin^{2}(a)} {2+cos^{2}(a)sin^{2}(a)}
=RHS
 
 
 
 
 
 
 
 
 
 
 
 
 

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 2 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available

Last Activity: 3 Years ago