Prove that,
(1-sinø+cosø)²=2(1+cosø)(1-sinø)
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Step-by-step explanation:
QUESTION -
(1+cotø-cosecø) (1+tanø+secø)=2
ANSWER -
Taking L.H.S,
=>
(1+CotØ-CosecØ)(1+tanØ+SecØ)
=>
(1+ CosØ/SinØ-1/SinØ)(1+SinØ/CosØ+1/CosØ)
=>
(SinØ+CosØ-1/SinØ)(CosØ+SinØ+1/CosØ)
=>
(SinØ+CosØ)²-1/SinØ.CosØ
=>
Sin²Ø+Cos²Ø+2SinØ.CosØ-1/SinØ.CosØ
=>
1+2SinØ.CosØ-1/SinØ.CosØ (Sin²Ø+Cos²Ø=1)
=>
1+2-1/1
=>
3-1
=>
2
R.H.S Proved
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