Question

Prove that (1+ tan ) 2+(1+ cot)2=
(sec + cosec) 2
please help me in this question

Answer 1

Answer:

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To Proof:-

( 1 - Tan)² + ( 1 - Cot)² = (Sec - Cosec)²

Proof:-

L.H.S

⟹ ( 1 - Tan)² + (1 - Cot)²

⟹ ( 1 - Sin/Cos)² + (1 - Cos/Sin)²

⟹ (Cos - Sin)²/Cos² + (Sin - Cos)²/Sin²

⟹ (Cos - Sin)² ( 1/Cos² + 1/Sin²)

⟹ (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²

⟹ (Cos - Sin)² /Cos²Sin²

⟹ ((Cos - Sin)/CosSin )²

⟹ (Cos/CosSin - Sin/CosSin)²

⟹ (1/Sin - 1/Cos)²

⟹ (Cosec - Sec)²

⟹ (Sec - Cosec)²

= R.H.S

HENCE PROVED!!

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Answer 2

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To Proof:-

( 1 - Tan)² + ( 1 - Cot)² = (Sec - Cosec)²

Proof:-

L.H.S

⟹ ( 1 - Tan)² + (1 - Cot)²

⟹ ( 1 - Sin/Cos)² + (1 - Cos/Sin)²

⟹ (Cos - Sin)²/Cos² + (Sin - Cos)²/Sin²

⟹ (Cos - Sin)² ( 1/Cos² + 1/Sin²)

⟹ (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²

⟹ (Cos - Sin)² /Cos²Sin²

⟹ ((Cos - Sin)/CosSin )²

⟹ (Cos/CosSin - Sin/CosSin)²

⟹ (1/Sin - 1/Cos)²

⟹ (Cosec - Sec)²

⟹ (Sec - Cosec)²

= R.H.S

HENCE PROVED!!

Answer 3

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To Proof:-

( 1 - Tan)² + ( 1 - Cot)² = (Sec - Cosec)²

Proof:-

L.H.S

⟹ ( 1 - Tan)² + (1 - Cot)²

⟹ ( 1 - Sin/Cos)² + (1 - Cos/Sin)²

⟹ (Cos - Sin)²/Cos² + (Sin - Cos)²/Sin²

⟹ (Cos - Sin)² ( 1/Cos² + 1/Sin²)

⟹ (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²

⟹ (Cos - Sin)² /Cos²Sin²

⟹ ((Cos - Sin)/CosSin )²

⟹ (Cos/CosSin - Sin/CosSin)²

⟹ (1/Sin - 1/Cos)²

⟹ (Cosec - Sec)²

⟹ (Sec - Cosec)²

= R.H.S

HENCE PROVED!!