Question

verify following trigonometric identities. 1/sec0tan0 = csc0 = sin0
check your typing, your statement is not true.
I figured you must mean

1/(secØtanØ) - cscØ = - sinØ

Proof:
LS = 1/((1/cosØ)(sinØ/cosØ)) - 1/sinØ
= cos^2 Ø/sinØ - 1/sinØ
= (cos^ Ø - 1)sinØ
= - sin^2 Ø/sinØ
= =sinØ
= RS

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