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inn [45]
3 years ago
15

prove tan(theta/2)=sin theta/1+cos theta for theta in quadrant 1 by filling in the calculations and reasons. PLEASE HELP!!!!

Mathematics
1 answer:
patriot [66]3 years ago
8 0

Answer:

See explanation

Step-by-step explanation:

We have to prove the identity

tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }

We will take right hand side of the identity

\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}

=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}

=tan(\frac{\Theta }{2}) [ Tan θ will be positive since θ lies in 1st quadrant ]

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