Question

sin 30°+ tan 45°- cosec 60°/ sec 30° + sin2 30°+ cos2 30°​

Answer 1

Question:-

๛Simplify:-

➜Sin30°+Tan45°-$\frac{Cosec60°}{Sec30°}$+Sin²30°+Cos²30°

$\rule{200}{1}$

AnsWer:-

☞$\frac{3}{2}$ or 1.5

$\rule{200}{1}$

Explanation:–

↝$\frac{1}{2}$+1-$\frac{Cosec60°}{Cosec(90-30)°}$+($\frac{1}{2}$)²+($\frac{\sqrt{3}}{2}$)²

↝$\frac{1+2}{2}$-$\frac{\cancel{Cosec60°}}{\cancel{Cosec60°}}$+$\frac{1}{4}$+$\frac{3}{4}$

↝$\frac{3}{2}$-1+$\frac{\cancel{4}}{\cancel{4}}$

↝$\frac{3-2}{2}$+1

↝½+1

↝$\frac{1+2}{2}$

↝$\frac{3}{2}$

$\rule{200}{2}$

Answer 2

Question :

• Evaluate : sin 30°+ tan 45°- cosec 60°/ sec 30° + sin² 30°+ cos² 30°

Solution :

$\implies \tt\sin 30 +\tan 45 - \frac{ \csc60}{ \sec30} + { \sin}^{2} 30 + { \cos}^{2} 30 \\ \\\tt\implies \dfrac{1}{2} + 1 - \dfrac{ \dfrac{2}{ \sqrt{3} } }{ \dfrac{2}{ \sqrt{3} } } + { \bigg (\dfrac{1}{2} \bigg)}^{2} + { \bigg(\frac{ \sqrt{3} }{2} \bigg)}^{2} \\ \\ \tt \implies \dfrac{1}{2} + 1 - \cancel{ \frac{2 \sqrt{3} }{2 \sqrt{3} }} + \dfrac{1}{4} + \dfrac{3}{4} \\ \\ \tt \implies \dfrac{2 + 4 - 4 + 1 + 3}{4} \\ \\ \tt \implies \dfrac{6}{4} \\ \\\tt \implies \dfrac{3}{2}$