if-sin-2-4-5-and-cos-2-3-5-prove-sin-cos-

Question Number 91038 by M±th+et+s last updated on 27/Apr/20

i f s i n (\frac{α}{2}) = \frac{4}{5}

a n d c o s (\frac{β}{2}) = \frac{3}{5}

p r o v e

s i n (α) = c o s (β)

Commented by jagoll last updated on 27/Apr/20

\sin α = 2 \sin (\frac{α}{2}) \cos (\frac{α}{2})

= 2 \times \frac{4}{5} \times \frac{3}{5} = \frac{24}{25}

\cos β = 2 \sin (\frac{β}{2}) \cos (\frac{β}{2})

= 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25}

Answered by $@ty@m123 last updated on 27/Apr/20

\sin^{2} \frac{α}{2} + \cos^{2} \frac{β}{2} = \frac{4^{2} + 3^{2}}{5^{2}}

\sin^{2} \frac{α}{2} + \cos^{2} \frac{β}{2} = 1

\Rightarrow \frac{α}{2} = \frac{β}{2}

\Rightarrow α = β