Mathematics, 12.07.2019 07:00 fields
Which double-angle or half-angle identity would you use to verify the following: cscxsecx=2csc2x a) cos2x=1-sin^2x b)sin2x=2sinxcosx c)tan2x=(2tanx)/(1-tan^2x) d)cos2x=2cos^2x-1
Answers: 1
![\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ csc(x)sec(x)=2csc(2x) \\\\[-0.35em] ~\dotfill\\\\ 2csc(2x)\implies 2\cdot \cfrac{1}{sin(2x)}\implies 2\cdot \cfrac{1}{2sin(x)cos(x)}\implies \cfrac{1}{sin(x)cos(x)} \\\\\\ \cfrac{1}{sin(x)}\cdot \cfrac{1}{cos(x)}\implies csc(x)sec(x)](/tpl/images/0080/0273/d983b.png)
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Which double-angle or half-angle identity would you use to verify the following: cscxsecx=2csc2x a)...
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