sec 2 A +cosec 2 A=13
If $ sec^2A + cosec^2A = 13,$ and A is an acute angle, then find the value of $ \text tan^2 A + cot^2A.$
यदि $ sec^2A + cosec^2A = 13,$ है तथा A एक न्यून कोण है, तो $ \text tan^2 A + cot^2A.$ का मान ज्ञात कीजिए
Detailed Solution & Logic
Correct Answer:
11
Given
$ \sec^2 A + \cosec^2 A = 13 $ and AAA is an acute angle.
Step 1: Use identities
We know,
$ \sec^2 A = 1 + \tan^2 A $
$ \cosec^2 A = 1 + \cot^2 A $
Substitute into the given equation:
$ (1+\tan^2 A) + (1+\cot^2 A) = 13 $
Step 2: Simplify
$ 2 + \tan^2 A + \cot^2 A = 13 $
$ \tan^2 A + \cot^2 A = 13 - 2 $
$ \tan^2 A + \cot^2 A = 11 $
✅ Final Answer: 11
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