Question

sin 6 A + cos 6 A + 3 sin square A + cos square is equals to 1​

Answer 1

Answer:We can also write question as :

$sin6a + cos6a = 1 - 3sin {a }^{2} + cos {a}^{2}$

Step-by-step explanation:

Solving LHS ,

°•° sin^6 A + cos^6 A.

= ( sin²A )³ + ( cos²A)³ .

[ Using Identity :- ( a³ + b³ ) = ( a + b )( a² + b² - ab ) . ]

= ( sin²A + cos²A )( sin⁴A + cos⁴A - sin²Acos²A ) .

= ( 1 )( sin⁴A + cos⁴A - sin²Acos²A + 2sin²Acos²A - 2sin²Acos²A ) .

[ °•° sin²A + cos²A = 1 ] .

= [ ( sin⁴A + cos⁴A + 2sin²Acos²A ) - 3sin²Acos²A ] .

= ( sin²A + cos²A )² - 3sin²Acos²A .

= 1² - 3sin²Acos²A .

= 1 - 3sin²Acos²A .

•°• LHS = RHS .

Hence, it is proved.