Question

if the cot B=12/5 prove that tan^2 B - sin^2 B = sin^4 B sec^2 B​

Answer 1

Answer:

Let, Side adjacent to angle B =AB = 12k Side opposite to angle B =BC = 5k where, k is any positive integer Firstly we have to find the value of AC. So, we can find the value of AC with the help of Pythagoras theorem ⇒ (AB)2 + (BC)2 = (AC)2 ⇒ (12k)2 + (5k)2 = (AC)2 ⇒ (AC)2 = 144 k2 +25 k2 ⇒ (AC)2 = 169 k2 ⇒ AC =√169 k2 ⇒ AC =±13k But side AC can’t be negative. So, AC = 13k Now, we will find the sin θ Now, LHS = RHS