prove that sin^2A + sin^2A × tan^2A= tan^2A
Answers
Answer:
Step-by-step explanation:
LHS
=> sin^2A + sin^2A x sin^2A .... ( tanA= sinA/cosA) cos^2A
=> sin^2A x cos^2A + (sin^2A sin^2A) .... ( LCM ) cos^2A
=> (1-cos^2A) (cos^2A) + sin^4A .... ( sin^2A= 1-cos^2A ) cos^2A
=> cos^2A - cos^4A + sin^4A
cos^2A
=> cos^2A - 1 ... (sin^4A+ cos^4A = 1) cos^2A
=> sin^2A ... ( cos^2A - 1 = sin^2A ) cos^2A
==> TAN^2A