Question

solve the following
(1+tan theta)^2 +1 -tan theta)^2=2 sec^2 theta​

Answer 1

Answer:

Proof below.....  Hope it helps! <3

Step-by-step explanation:

$(1+\tan\theta)^2+(1-\tan\theta)^2\\=1+\tan^2\theta+2\tan\theta+1+\tan^2\theta-2\tan\theta\\=\sec^2\theta+\sec^2\theta\\=2\sec^2\theta$∵ 1+tan²θ = sec²θ

Hence proved.

Answer 2

Step-by-step explanation:

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

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

since, 1+tan^2theta= sec^2

.°. sec^2 + sec^2 +2tan theta - 2 tan theta

= 2sec^2theta