Question

prove that. sin^4 A+sin²Acos²A=sin²A​

Answer 1

Answer:

property : Sin²A + Cos²A = 1

Step-by-step explanation:

Sin⁴A + Sin²A*Cos²A

Sin²A ( Sin²A + Cos²A )

Sin²A * 1 = Sin²A

( Hence proof )

Answer 2

Question :

prove that :

$\sin {}^{4} (x) + \sin {}^{2} (x) \cos {}^{2} (x)$

Trignometric Formulas:

1. sin²A + cos²A = 1
2. sec²A - tan²A = 1
3. cosec²A - cot²A = 1
4. sin2A = 2 sinA cosA
5. cos2A = cos²A - sin²A

$\huge{ \underline{ \underline{ \green{ \sf{ Detailed \: Answer :}}}}}$

LHS :

$\sin {}^{4} (x) + \sin {}^{2} (x) \cos {}^{2} (x)$

take sin²x common from equation:

$= \sin {}^{2} (x) ( \sin {}^{2} (x) + \cos {}^{2} (x) )$

we know that sin²A + cos²A = 1

________________

$= \sin {}^{2} (x)$

RHS

$= \sin {}^{2} (x)$

⇒LHS = RHS

$\huge{\bold{ Hence \: Proved }}$