Prove that sec*2 theeta + cosec*2 theeta =sec*2 theeta x cosec*2 theeta?

2 Answers
Mar 1, 2018

Proved in explanation...

Explanation:

#sec^2 theta+cosec^2theta# can be written as

#1/cos^2theta + 1/sin^2theta#

Taking lcm

#(sin^2theta+cos^2 theta)/(sin^2 theta*cos^2theta)#

#color (blue)("recall" sin^2 A+Cos^2 A=1)#

#1/(sin^2 theta* cos^2 theta)#

#1/sin^2theta *1/cos^2theta#

#cosec^2 theta×sec^2 theta#
Hence proved

Mar 1, 2018

See below.

Explanation:

I am reading this as:

#sec^2(theta)+csc^2(theta)=sec^2(theta)csc^2(theta)#

Identities:

1) #color(red)bb(sec^2(x)=1/cos^2(x))#

2) #color(red)bb(csc^2(x)=1/sin^2(x))#

3) #color(red)bb(sin^2x+cos^2x=1)#

#LHS#

#sec^2(theta)+csc^2(theta)#

Using identities 1 and 2:

#1/cos^2(theta)+1/sin^2(theta)#

Add fractions:

#(sin^2(theta)+cos^2(theta))/(cos^2(theta)sin^2(theta))#

Using identity 3

#1/(cos^2(theta)sin^2(theta))#

By identities 1 and 2:

#sec^2(theta)csc^2(theta)#

#LHS-=RHS#