Question

( sec θ / sec θ + tan θ ) + ( tan θ / sec θ - tan θ )

Answer 1

Answer:

0

i hope you helpfull this ans

Answer 2

Step-by-step explanation:

sec theta / sec theta + tan theta

sec theta (sec theta - tan theta)

= ---------------------------------------------------------

(sec theta+tan theta)(sec theta-tan theta)

sec theta(sec theta - tan theta)

= ---------------------------------------------

sec^2theta - tan^2 theta

= sec theta(sec theta - tan theta) ========>(1)

similarly, tan theta/(sec theta - tan theta)

tan theta(sec theta + tan theta)

= ------------------------------------------------------------

(sec theta - tan theta)(sec theta+tan theta)

tan theta(sec theta+tan theta)

= ----------------------------------------------

sec^2 theta - tan^2 thetasec theta

= tan theta(sec theta + tan theta) ======> (2)

(1)+(2) ====>

sec theta(sec theta - tan theta)+tan theta(sec theta+tan theta)

=sec^2 theta - (sec theta)(tan theta)+(tan theta)(sec theta)+tan^2 theta

= sec^2 theta + tan^2 theta

= (1+tan^2 theta)+tan^2 theta

= 1+2tan^2 theta

hope it helps you

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