QUESTION OF TRIGONOMETIC IDENTITIES
Prove that:
Sec^6theta = tan^6theta + 3tan^2theta× sec^2theta + 1
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||✪✪ QUESTION ✪✪||
Prove that:
Sec^6theta = tan^6theta + 3tan^2theta× sec^2theta + 1
|| ✰✰ ANSWER ✰✰ ||
Taking LHS, we get,
→ sec^6A
→ (sec²A)³
Now, using sec²A = 1 + Tan²A we get,
→ (1 + Tan²A)³
Now, using (a+b)³ = a³ + b³ + 3ab(a+b) we get,
→ (1)³ + (Tan²A)³ + 3 * 1 * Tan²A (1 + Tan²A)
Again, using (1+tan²A) = sec²A we get,
→ 1 + Tan^6A + 3Tan²A*sec²A
→ Tan^6A + 3Tan²A*sec²A + 1 = RHS .
Hence Proved .
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