Prove that cos( 3π/ 2 + ) cos(2 + ) [cot ( 3π/2 - ) + cot(2 + )]=1.
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1
Answer:
L.H.S.=cos(
2
3π
+x)cos(2π+x)[cot(
2
3π
−x)+cot(2π+x)]
=sinxcosx[tanx+cotx]
=sinxcosx(
cosx
sinx
+
sinx
cosx
)
=(sinxcosx)[
sinxcosx
sin
2
x+cos
2
x
]
=1=R.H.S.
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