Question

162) tan^2 60 +4cos² 45+ 3 cosec^2
60+3 cos^2 90/
2 cosec 30 + 3 sec 60 - 7/3 cot^2 30
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Answer 1

Answer:

2.5

Step-by-step explanation:

I assume the task is $\frac{tan^260+4cos^245+3cosec^260+3cos^290}{2cosec30+3sec60-(7/3)cot^230}$

1). tan 60° = √3 ⇒ tan² 60° = 3

2). cos 45° = √2/2 ⇒ cos² 45° = 1/2

3). cosec 60° = 2/√3 ⇒ 3cosec² 60° = 3(2/√3)² = 4

4). cos 90° = 0

The numerator is 3 + 1/2 + 4 + 0 = $7\frac{1}{2}$ = 15/2

5). cosec 30° = 2 ⇒ 2cosec 30° = 4

6). sec 60° = 2 ⇒ 3sec 60° = 6

7). cot 30° = √3 ⇒ (7/3)cot²30° = 7

The denominator is 4 + 6 - 7 = 3

$\frac{15}{2}$ ÷ 3 = $\frac{15}{2}$ × $\frac{1}{3}$ = 5/2 = 2.5