Question

prove that sec2 20° = 1+tan2 20° ​

Answer 1

hope it helps you..........

Answer 2

Answer:

it is proven that $sec ^{2}$ 20° = 1 + $tan ^{2}$ 20°  

Step-by-step explanation:

Given problem is prove that $sec^{2} 20$° = 1 + $tan^{2} 20$°  

take trigonometric identity  at θ = 20° ⇒ $sin^{2}$ 20° + $cos^{2}$ 20° = 1

⇒  $sin^{2}$ 20° +  $cos^{2}$ 20° =  1

divide with $cos^{2}$ 20° on both sides

 ⇒  $sin^{2}$20°/ $cos ^{2}$20° + $cos ^{2}$ 20° = 1/ $cos^{2}$ 20°

 ⇒ $tan ^{2}$ 20° + 1 = $sec ^{2}$ 20°   [ $sin ^{2}$20°/ $cos^{2}$ 20° = $tan^{2}$20° , 1/$cos^{2}$20° = $sec^{2} 20$]

 ⇒ It is proven that   $sec ^{2}$20° = 1 + $tan ^{2}$ 20°