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**Q****) If sin A = and cos B = , then find the value of (tan A + tan B)**

**Ans: **We To find the value of tan A + tan B, we need to find the value of tan A and tan **B**

**Step 1:** We are given sin A =

We know that sin^{2} A + cos^{2} A = 1

∴ ()^{2} + cos^{2} A = 1

∴ cos^{2} A = 1 –

∴ cos A =

Now, tan A =

By substituting value of sin A and cos A in above equation, we get:

tan A =

**Step 2:** Next, we have cos B =

∵ sin^{2} B + cos^{2} B = 1

∴ sin^{2} B + ()^{2} = 1

∴ sin^{2} B = 1 –

∴ sin B =

Now, tan B =

By substituting value of sin B and cos B in above equation, we get:

tan A =

Step 3: Let’s find the value of (tan A + tan B) by substituting the values from step 1 and step 2:

(tan A + tan B) =

=

**Therefore, the value of (tan A + tan B) is **

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