How do you verify the identify #tan^2theta+1=sec^2theta#?

1 Answer
Jim G.
Aug 3, 2016

see explanation

Explanation:

The following #color(blue)"trigonometric identies"# are 'useful'

#color(orange)"Reminders"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(tantheta=(sintheta)/(costheta))color(white)(a/a)|)))#

#color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2theta+cos^2theta=1)color(white)(a/a)|)))" and " color(red)(|bar(ul(color(white)(a/a)color(black)(sectheta=1/costheta)color(white)(a/a)|)))#

the left side #=tan^2theta+1=(sin^2theta)/(cos^2theta)+(cos^2theta)/(cos^2theta)#

Expressing as a single fraction gives.

#(sin^2theta+cos^2theta)/(cos^2theta)=1/(cos^2theta)=sec^2theta="right side hence verified"#

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