Question

solve the equation
1) 1-2Cos^2 60°+Sin30°
2) 2tan^2 30°-tan^2 45° +tan^2 60°
trignometry question

Answer 1

Solution 1 :

$\boxed{ \sf 1 - 2 { \cos}^{2} 60° + \sin30°} \\ \\ \implies \sf 1 - 2 { \bigg (\dfrac{1}{2}\bigg) }^{2} + \frac{1}{2} \\ \\ \implies 1 - 2 \times \frac{1}{4} + \frac{1}{2} \\ \\ \implies1 - \frac{1}{2} + \frac{1}{2} \\ \\ \implies 1 - 1 \\ \\ \implies 0$

Solution 2 :

$\boxed{ \sf 2 { \tan }^{2} 30° - { \tan }^{2} 45° + { \tan}^{2} 60° }\\ \\ \implies \sf 2 {\bigg( \frac{1}{ \sqrt{3} } \bigg)}^{2} - {(1)}^{2} + {\bigg( \sqrt{ 3} \bigg) }^{2} \\ \\ \implies \sf \frac{2}{3} - 1 + 3 \\ \\ \implies \sf \frac{2 - 3 + 9}{3} \\ \\ \implies \sf \frac{8}{3}$