Question

(i) sin 30° + tan 45º - cosec 60°
sec 30° + cos 60° + cot 45°
​

Answer 1

$\large \bold \green{ \underline{answer = \frac{5}{3} }}$

Step-by-step explanation:

$\large \bold{ \underline{question}} \\ 1) = \sin(30) {}^{0} + \tan(45) {}^{0} - \csc(60 ){}^{0}. \sec(30) {}^{0} + \cos(60) {}^{0} + \cot(45) {}^{0} \\ = \frac{1}{2} + 1 - \frac{2}{ \sqrt{3} } \times \frac{2}{ \sqrt{3} } + \frac{1}{2} + 1 \\ \\ = \frac{1}{2} + 1 - \frac{4}{3} + \frac{1}{2} + 1 \\ \\ = \frac{3 + 6 - 8 + 3 + 6}{6} \\ \\ = \frac{10}{6} = \frac{5}{3}$

Answer 2

QUESTION:

(i) sin 30° + tan 45º - cosec 60°

sec 30° + cos 60° + cot 45°

ANSWER:

We use the trigonometry identity here;

1.

$\sin(30) = \frac{1}{2}$

2.

$\tan(45) = 1$

3.

$\csc(60) = \frac{2}{ \sqrt{3} }$

4.

$\sec(30) = [tex]\frac{2}{ \sqrt{3} }$

5.

$\cos(60) = \frac{1}{2}$

6.

$\cot(45) = 1$

now come to main question;

$\sin(30) + \tan(45) - \csc(60) \times \sec(30) + \cos(60) + \cot(45)$

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

$\frac{1}{2} + 1 - \frac{2}{ \sqrt{3} } \times \frac{2}{ \sqrt{3} } + \frac{1}{2} + 1$

$(taking \: lcm)$

$\frac{3 + 6 - 8 + 3 + 6}{6}$

$\frac{10}{6}$

$(in \: simplest \: form)$

$\frac{5}{3}$

FINAL ANSWER :

$\huge\red {\frac{5}{3} }$