If (x + 2y) = 90°, then, find the value of [tanx/cot2y + 3tan(x + y)/coty + 8tan(x – y)/cot3y + 3]?

- 10
- 11
- 15
- 12

Option 3 : 15

**Given:**

[tanx/ cot2y + 3tan(x + y)/coty + 8tan(x – y)/cot3y + 3]

**Formula Used:**

tan(90° - x) = cotx

**Calculation:**

x + 2y = 90°

Therefore, x = (90° - 2y); (x + y) = (90° - y); (x – y) = (90° - 3y)

[tanx/cot2y + 3tan(x + y)/coty + 8tan(x – y)/cot3y + 3]

⇒ [tan(90° - 2y)/cot2y + 3tan(90° - y)/coty + 8tan(90° – 3y)/cot3y + 3]

⇒ cot2y/cot2y + 3coty/coty + 8cot3y/cot3y + 3

⇒ 1 + 3 + 8 + 3

⇒ 15

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