sin square theta by cos square theta + cos square theta by sin square theta is equal to secant square theta minus cos cosec square theta minus 2
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Sin²θ/Cos²θ + Cos²θ/Sin²θ = Sec²θ + Cosec²θ - 2
Step-by-step explanation:
Correct Questio is
Sin²θ/Cos²θ + Cos²θ/Sin²θ = Sec²θ + Cosec²θ - 2
LHS = Sin²θ/Cos²θ + Cos²θ/Sin²θ
= (Sin⁴θ + Cos⁴θ)/Cos²θSin²θ
= ((Sin²θ + Cos²θ)² - 2 Sin²θCos²θ )/Cos²θSin²θ
= (1² - 2 Sin²θCos²θ )/Cos²θSin²θ
= 1/Cos²θSin²θ - 2
= (Sin²θ + Cos²θ)/Cos²θSin²θ - 2
= Sin²θ/Cos²θSin²θ + Cos²θ/Cos²θSin²θ - 2
= 1/Cos²θ + 1/Sin²θ - 2
= Sec²θ + Cosec²θ - 2
= RHS
QED
Proved
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