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If sin37^(@)=z, express sin74^(@) in ter...

If `sin37^(@)=z`, express `sin74^(@)` in terms of z.

A

`2zsqrt(1-z^2)`

B

`2z^(2)+1`

C

`2z`

D

`2z^(2)-1`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin74^(@)=2sin37^(@)cos37^(@)`. Since `sin^(2)z+cos^(2)z=1, cosz=+-sqrt(1-sin^(2)z)`, and `74^(@)` is in the first quadrant, the positive square root applies, so cos `z=sqrt(1-z^(2))`. Therefore, `sin74^(@)=2sin37^(@)sqrt(1-sin^(2)37^(@))=2zsqrt(1-z^(2))`
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