MCQ
If $(\tan\theta+\cot\theta)=5$ then $(\tan^2\theta+\cot^2\theta)=?$
- A$27$
- B$25$
- C$24$
- ✓$23.$
✓
Answer
Correct option: D.
$23.$
$(\tan\theta+\cot\theta)=5$
$\Rightarrow(\tan\theta+\cot\theta)^2=5^2$
$\Rightarrow\tan^2\theta+\cot^2\theta+2\tan\theta\cot\theta=25$
$\Rightarrow\tan^2\theta+\cot^2\theta+2(1)=25$
$\Rightarrow\tan^2\theta+\cot^2\theta=23$
$\Rightarrow(\tan\theta+\cot\theta)^2=5^2$
$\Rightarrow\tan^2\theta+\cot^2\theta+2\tan\theta\cot\theta=25$
$\Rightarrow\tan^2\theta+\cot^2\theta+2(1)=25$
$\Rightarrow\tan^2\theta+\cot^2\theta=23$
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