Introduction to Trigonometry Test

Result

Introduction to Trigonometry Test - 4

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Question 1
1 / -0

If sin x + sin² x = 1, then find the value of cos⁴ x + cos⁸ x + 2 cos⁶ x + 1.

A
-1

B
0

C
1

D
2

Solution

sin x = 1 - sin² x = cos² x
cos⁴ x + cos⁸ x + 2cos⁶x + 1
= sin² x + sin⁴x + 2 sin³ x + 1
= (sin x + sin²x)² + 1
= 2
Question 2
1 / -0

What is the value of q if cot(p + q – r + s) = 0, sin(p – q) = 1/2, cosec(q + s) = √2 and sec(q + r) = 1?

A
9.5°

B
8.7°

C
7.5°

D
6°

Solution

cot(p + q – r + s) = 0
cot(p + q – r + s) = cot 90°
Therefore, (p + q – r + s) = 90° --- (1)
Now, sin(p – q) = 1/2

sin(p – q) = sin 30°
So,(p – q) = 30° --- (2)

Also, cosec(q + s) = √2
cosec(q + s) = cosec 45°
(q + s) = 45° --- (3)

And sec(q + r) = 1
sec(q + r) = sec 0°
(q + r) = 0° --- (4)

Now, adding equations (2) and (4),
p + r = 30° --- (5)

Now, putting (3) in (1),
So, p – r = 90° - 45° = 45° --- (6)

Now, subtracting equation (6) from equation (5),
2r = -15°
r = -7.5°

Now, putting r = -7.5° in equation (4), we get
q = 7.5°