sec ⁴-theta - tan⁴theta =1+2tan²theta
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Explanation:
Left Hand Side:
Use the identity:
1+tan² θ = sec² θ
sec ⁴ θ − tan⁴ θ = ( sec ²θ - tan ² θ ) ( sec ² θ + tan ² θ )
=1 (sec²θ + tan²θ )
=sec²θ + tan²θ
=1 + tan²θ + tan²θ
=1 + 2 tan²θ
∴ Right Hand Side = 1 + 2 tan²θ
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