Question

${cos \: a \: }^{4} - {sin}^{4} a \: + 1 = 2cos^{2} a$
prove

Answer 1

Hello... ☺


please refer to the attachment above....


thank you ☺

Answer 2

HEY THERE !!!!

Formula:-

Sin²a+Cos²a=1

Sin²a=1-Cos²a

cos²a=1-Sin²a

According to the Question!!

Question:-

Cos⁴a-Sin⁴a +1 = 2cos²a

Solution:-

(cos²a)²-(Sin²a)²

Using identity a⁴-b⁴=(a²)²-(b²)²

=>(cos²a)²-(Sin²a)²

=>(Cos²a-Sin²a)(Cos²a+Sin²a)

=>Cos²a-Sin²a(1)

=>Cos²a-Sin²a

=> 2cos²a