Question

State the correctness of the following identity
${\sec }^6\theta =1+3{\tan }^2\theta {\sec }^2\theta +{\tan }^6\theta$

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient

Answer 1

Answer: (A)

Yes

$se{c}^6\theta$
$=(se{c}^2\theta {)}^3$
$=(1+ta{n}^2\theta {)}^3$ ....($se{c}^2\theta =1+ta{n}^2\theta$)
$=1+ta{n}^6\theta +3ta{n}^2\theta (1+ta{n}^2\theta )$
$=1+ta{n}^6\theta +3ta{n}^2\theta se{c}^2\theta$
$=RHS$
Hence proved.