Question

sin 30° + tan 45º – cosec 60°
sec 30° + cos 60° + cot 45°​

Answer 1

Question:

I) sin30° + tan45° - cosec60°

II) sec30° + cos60° + cot45°

Answer:

Using

sin30° = 1/2tan45° = 1

cosec60° = 2/√3

Substituting we get

I) solution

$= { \sin}30^{ \circ} + { \tan45}^{ \circ} - { \csc60}^{ \circ } \\ \\ = \dfrac{1}{2} + 1 - \dfrac{2}{ \sqrt{3} } \\ \\ = \frac{3}{2} - \frac{2}{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} - 4 }{2 \sqrt{3} }$

Using

sec30° = 2/√3

cos60° = 1/2

cot45° = 1

Substituting

We get

$= { \sec30}^{ \circ} + { \cos60}^{ \circ} + { \cot45}^{ \circ} \\ \\ = \frac{2}{ \sqrt{3} } + \frac{1}{2} + 1 \\ \\ = \frac{3}{2} + \frac{2}{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} + 4 }{2 \sqrt{3} }$