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5. Prove : tan²0 + cot²0 + 2 = sec²0.cosec²0. |
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Answer» Step-by-step EXPLANATION: To prove -----> tan²θ + Cot²θ + 2 = Sec²θ Cosec²θ Proof-----> LHS= tan²θ + Cot²θ + 2 Multiplying and dividing by tanθ in third TERM , we GET, = ( tanθ )² + ( Cotθ )² + 2 tanθ ( 1 / tanθ ) We KNOW that , Cotθ = 1 / tanθ , applying it we get, = ( tanθ )² + ( Cotθ )² + 2 tanθ Cotθ We know that, a² + b² + 2ab = ( a + b )² , applying it , we get, = ( tanθ + Cotθ )² We know that, tanθ = Sinθ / Cosθ , Cotθ = Cosθ / Sinθ , applying it we get, = { ( Sinθ / Cosθ ) + ( Cosθ / Sinθ ) }² = { ( Sin²θ + Cos²θ ) / Sinθ Cosθ }² We know that, Sin²θ + Cos²θ = 1 , applying it we get, = ( 1 / Sinθ Cosθ )² = 1 / Sin²θ Cos²θ = ( 1 / Sin²θ ) ( 1 / Cos²θ ) We know that , 1 / Sinθ = Cosecθ , 1 / Cosθ = Secθ , applying it , we get, = Cosec²θ Sec²θ = RHS |
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