Question

sec@-tan@/sec@+tan@=1-2sec@tan@+2tan^2@ prove it

Answer 1

here is the answer,,, sorry for bad quality pic!!!

Answer 2

Heya...!!!



(SecФ - tanФ) / (secФ + tanФ)

⇒(secФ - tanФ) / (secФ + tanФ) × (secФ - tanФ) / (secФ - tanФ)

⇒(secФ - tanФ)² / (sec²Ф - tan²Ф)

⇒(sec²Ф + tan²Ф - 2secФtanФ) / (1)
∴ [ sec²Ф - tan²Ф = 1 ]

⇒(1 + tan²Ф) + tan²Ф - 2secФtanФ
∴ [ sec³Ф = 1 + tan²Ф ]

⇒1 + 2tan²Ф - 2secФtanФ

⇒1 - 2secФtanФ + 2tan²Ф


Hence,

L.H.S = R.H.S



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