Question

Th value of $(\sin \theta +\csc \theta {)}^2+(\cos \theta +\sec \theta {)}^2-({\tan }^2\theta +{\cot }^2\theta )$ is

• A. $1$
• B. $2$
• C. $6$
• D. $7$

Answer 1

Answer: (D)

$7$

By expanding the expression we get

$(\sin \theta +\csc \theta ){}^2+(\cos \theta +sec\theta ){}^2-({\tan }^2\theta +co{t}^2\theta )$

$={\sin }^2\theta +{\csc }^2\theta +2+se{c}^2\theta +{\cos }^2\theta +2-{\tan }^2\theta -co{t}^2\theta$

$=4+({\sin }^2\theta +{\cos }^2\theta )+({\csc }^2\theta -co{t}^2\theta )+(se{c}^2\theta -{\tan }^2\theta )$

$=4+1+1+1=7$

Hence answer is D