Question

without using trigonometric table
please help me to do this sum​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given expression is }\dfrac{cos70}{sin20} + \dfrac{cos59}{sin31} - 8sin^{2}30 = 0$

       $\text{Taking L.H.S}$

$\implies\dfrac{cos70}{sin20} + \dfrac{cos59}{sin31} - 8sin^{2}30$

       $\text{We know that, }sin\theta = cos(90-\theta)$

$\implies sin20 = cos(90-20) = cos70$

$\implies sin31 = cos(90-31) = cos59$

       $\text{Substituting in the expression}$

$\implies \dfrac{cos70}{cos70} + \dfrac{cos59}{cos59} - 8sin^{2}30$

$\implies 1 + 1 - 8sin^{2}30$

$\implies 2 - 8sin^{2}30$

       $\text{We know that, }sin30 = \dfrac12$

$\implies 2 - 8(\dfrac12)^{2}$

$\implies 2 - 8(\dfrac14)$

$\implies 2 - 2$

$\implies 0$

$\implies \text{L.H.S = R.H.S}$

       $\text{Hence proved}$