Question

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

Answer 1

$\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ csc(x)sec(x)=2csc(2x) \\\\[-0.35em] ~\dotfill\\\\ 2csc(2x)\implies 2\cdot \cfrac{1}{sin(2x)}\implies 2\cdot \cfrac{1}{2sin(x)cos(x)}\implies \cfrac{1}{sin(x)cos(x)} \\\\\\ \cfrac{1}{sin(x)}\cdot \cfrac{1}{cos(x)}\implies csc(x)sec(x)$

Answer 2

Answer:

OPTION B.

Step-by-step explanation: