Question

prove this please i request everybody​

Answer 1

$\begin{aligned}&\text{LHS}\\\\\implies\ \ &\sin^25\textdegree+\sin^210\textdegree+\sin^215\textdegree+\ \dots\ +\sin^240\textdegree+\sin^245\textdegree+\sin^250\textdegree+\ \\&\dots\ +\sin^285\textdegree+\sin^290\textdegree\\\\\implies\ \ &\sin^25\textdegree+\sin^210\textdegree+\sin^215\textdegree+\ \dots\ +\sin^240\textdegree+\sin^250\textdegree+\ \\&\dots\ +\sin^285\textdegree+1+\dfrac{1}{2}\end{aligned}$

$\begin{aligned}\implies\ \ &\sin^25\textdegree+\sin^210\textdegree+\sin^215\textdegree+\ \dots\ +\sin^240\textdegree+\cos^240\textdegree+\ \\&\dots\ +\cos^25\textdegree+1\dfrac{1}{2}\quad\quad\left[\because\ \sin^2(90\textdegree-x)=\cos^2x\right]\\\\\implies\ \ &\underbrace{\sin^25\textdegree+\cos^25\textdegree+\sin^210\textdegree+\cos^210\textdegree+\!\dots\!+\sin^240\textdegree+\cos^240\textdegree}_{16}+1\dfrac{1}{2}\end{aligned}$

$\begin{aligned}\implies\ \ &\underbrace{1+1+1+\dots+1}_{8}+1\dfrac{1}{2}\\\\\implies\ \ &8+1\dfrac{1}{2}\\\\\implies\ \ &9\dfrac{1}{2}\\\\\implies\ \ &\text{RHS}\end{aligned}\\\\\\\\\huge\textsc{\underline{\underline{Hence Proved!}}}$

Answer 2

Step-by-step explanation:

9½

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hope it helps