Verify: #(1+tan^2 theta)(1-sin^2 theta)=1#?

2 Answers
Somebody N.
Jan 3, 2018

See below.

Explanation:

Identities:

#color(red)(1+tan^2x=sec^2x)#

#color(red)(secx=1/cosx)#

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

#1+tan^2(theta)=sec^2(theta)=1/(cos^2(theta))=1/(1-sin^2(theta)#

#(1/(1-sin^2(theta)))(1-sin^2(theta))=1#

Alan N.
Jan 3, 2018

See below.

Explanation:

To verify: #(1+tan^2 theta)(1-sin^2 theta)=1#

Remember that: #sin^2theta + cos^2theta =1 -> (1-sin^2theta) = cos^2theta#

Hence, LHS#= (1+tan^2theta)*cos^2theta#

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

#= cos^2theta + sin^2theta#

#=1 =# RHS

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