Question

1/ cos2 30 + 1/ sin3 30 +1/2 tan2 45 -8 sin2 90

Answer 1

Answer:

- 145/24

Step-by-step explanation:

1/cos^2 30° +1/sin^3 30° +1/ 2tan^2 45° -8sin^2 90°

cos 30° = root 3/ 2

sin 30° = 1/2

tan 45° = 1

sin 90° = 1

= 1/ (root3 /2)^2 + (1/2)^3 + 1/2 - (8×1)

= 1/ (3/4) + 1/8 +1/2 - 8

= 4/3 + 1/8 + 1/2 - 8

= 32/24 + 3/24 + 12/24 - 192/24

= - 145/24

Answer 2

Given $\frac{1}{cos^230}+\frac{1}{sin^330}+\frac{1}{2tan^245}-8sin^290$

We need to find the value of the given expression

We know

$cos30=\frac{\sqrt{3}}{2}, \\sin30=\frac{1}{2},\\tan45=1\\sin90=1$

Substitute the values and we get

$=\frac{4}{3}+\frac{8}{1}+\frac{1}{2}-8 \times 1\\=\frac{8+48+3-48}{6}\\=\frac{8+3}{6}\\=\frac{11}{6}$

Therefore, the required answer is $\frac{11}{6}$ .

To learn more about the trigonometric function

https://brainly.in/question/1013629

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