Q)  Prove that 1 + tan ² A = sec ² A

Ans: 

Step 1: Let’s draw a right angled triangle:

Here ABC is a triangle where ∠ B is right angle.

Step 2: By applying Pythagoras theorem, we know:

AB ²  + BC ²  = AC ²

Step 3: Let’s divide the above equation by AB on both sides, we get:

∴

∴

Step 4: Now, by observation, in the above diagram:

and

Step 5: By substituting 2  values in the above equation, we get:

Existing equation:

∴ 1 + tan ² A = sec ² A

Hence Proved !

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