Question

Sin 30°+Tan 45°−Cosec 60°
Sec 30°+Cos 60°+Cot 45°

Answer 1

Step-by-step explanation:

1) Sin30° + tan45° - Cosec60°

= 1/2 + 1 - 2/√3

= (3√3 - 4)/2√3

2) Sec30° + cos60° + cot45°

= 2/√3 + 1/2 + 1

= (4 + 3√3)/2√3

Answer 2

Correct Question :-

sin30° + tan45° - cosec60°/ sec30° + cos60° + cot45°

Solution :-

$\rm\longrightarrow\dfrac{\dfrac{1}{2}+1-\dfrac{2}{\sqrt{3}}}{\dfrac{2}{\sqrt{3}}+\dfrac{1}{2}+1}$

$\rm\longrightarrow\dfrac{\dfrac{\sqrt{3}+2\sqrt{3}-4}{2\sqrt{3}}}{\dfrac{4+\sqrt{3}+2\sqrt{3}}{2\sqrt{3}}}$

$\rm\longrightarrow\dfrac{\dfrac{3\sqrt{3}-4}{2\sqrt{3}}}{\dfrac{3\sqrt{3}+4}{2\sqrt{3}}}$

$\rm\longrightarrow\:\dfrac{3\sqrt{3}-4}{\cancel{2\sqrt{3}}}\times\:\dfrac{\cancel{2\sqrt{3}}}{3\sqrt{3}+4}$

$\rm\longrightarrow\:\dfrac{3\sqrt{3}-4}{3\sqrt{3}+4}$

➥ Rationalize the denominator

$\rm\longrightarrow\:\dfrac{(3\sqrt{3}-4)}{(3\sqrt{3}+4)}\times\dfrac{(3\sqrt{3}-4)}{(3\sqrt{3}-4)}$

$\rm\longrightarrow\:\dfrac{(3\sqrt{3}-4)^2}{(3\sqrt{3})^2-{(4)}^{2}}$

$\rm\longrightarrow\:\dfrac{(3\sqrt{3})^2-2\times\:3\sqrt{3}\times\:4+{(4)}^{2}}{(3\sqrt{3})^2-{(4)}^{2}}$

$\rm\longrightarrow\:\dfrac{27-24\sqrt{3}+16}{27-16}$

$\rm\longrightarrow\:\dfrac{43-24\sqrt{3}}{11}$

Hence,the Solution will be $\rm\:\dfrac{43-24\sqrt{3}}{11}$