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