**Trigonometry Questions Worksheet for Grade 11 :**

Here we are going to see some example problems on trigonometry to understand the method of proving trigonometric problems.

**Question 1 :**

Show that

(i) tan(45° + A) = (1 + tanA)/(1 − tanA)

(ii) tan(45° − A) = (1 + tanA)/(1 − tanA)

**Solution :**

(i) tan(45° + A) = (1 + tanA)/(1 − tanA)

**tan (A + B) = (tan A + tan B) / (1 - tan A tan B)**

= (tan 45° + tan A) / (1 - tan 45° tan A)

The value of tan 45° is 1.

= (1 + tan A) / (1 - tan A)

(ii) tan(45° − A) = (1 + tanA)/(1 − tanA)

**Solution :**

**tan (A - B) = (tan A - tan B) / (1 + tan A tan B)**

= (tan 45° - tan A) / (1 + tan 45° tan A)

The value of tan 45° is 1.

= (1 - tan A) / (1 + tan A)

**Question 2 :**

Prove that cot(A + B) = (cotAcotB − 1)/(cotA + cotB)

**Solution :**

L.H.S

cot(A + B) = cos (A + B) / sin (A + B)

= (cos A cos B - sin A sin B) / (sin A cos B + cos A sin B)

By dividing every terms by sin A sin B, we get

= (cot A cot B - 1) / (cot B + cot A)

= (cot A cot B - 1) / (cot A + cot B) ---> R.H.S

Hence proved.

**Question 3 :**

If tan x = n/(n + 1) and tan y = 1/(2n + 1) , find tan(x + y).

**Solution :**

tan(x + y) = (tan x + tan y) / (1 - tanx tan y)

= n(2n + 1) + (n + 1) / (n + 1)(2n + 1) - n

= (2n^{2} + n + n + 1) / (2n^{2} + n + 2n + 1 - n)

= (2n^{2} + 2n + 1) / (2n^{2} + 2n + 1)

tan(x + y) = 1

Hence the value of tan(x + y) is 1.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems in trigonometry.

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