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# P2/P3 make RHS = LHS watch

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1. The question is: Show that the LHS is equal to the RHS.

4cos 2x / sin^2 2x = cosec^2x - sec^2x

How do you do this?
2. (Original post by BlueAngel)
The question is: Show that the LHS is equal to the RHS.

4cos 2x / sin^2 2x = cosec^2x - sec^2x

How do you do this?
make top: 4(cos^2x - sin^2x)
make bottom: (2sinx.cosx)^2 = 4(sinx)^2.(cosx)^2

4's cancel, and you're left with:

[cos^2x - sin^2x] / (sin^2x)(cos^2x)

now split up the fraction:

[cos^2x / (sin^2x)(cos^2x)] - [sin^2x / (sin^2x)(cos^2x)]

the numerator of each fraction cancels with its corresponding term on the denominator to leave:

cosec^2x - sec^2x
3. (Original post by mockel)
make top: 4(cos^2x - sin^2x)
make bottom: (2sinx.cosx)^2 = 4(sinx)^2.(cosx)^2

4's cancel, and you're left with:

[cos^2x - sin^2x] / (sin^2x)(cos^2x)

now split up the fraction:

[cos^2x / (sin^2x)(cos^2x)] - [sin^2x / (sin^2x)(cos^2x)]

the numerator of each fraction cancels with its corresponding term on the denominator to leave:

cosec^2x - sec^2x

thank you very much.
4. (Original post by BlueAngel)
thank you very much.
np

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