Question

sin⁴ø-cos⁴ø-1/sin²ø-cos²ø+1​

Answer 1

Answer:

cos⁴ø - sin⁴ø = 1/2

=>( cos²ø)² - (sin²ø)² = 1/2

=>(cos²ø - sin²ø)(cos²ø + sin²ø)=1/2

=>( cos²ø - sin²ø )×1 = 1/2

=> cos²ø - sin²ø = 1/2

=> cos2ø = 1/2

=> cos 2ø = cos 60°

=> 2ø = 60°

=> ø = 30°

Answer 2

Answer:

LHS =

$\frac{ \sin {}^{4} (x) - \cos {}^{4} (x) + 1 }{ \sin {}^{2} (x) - \cos {}^{2} (x) + 1}$

we know that

sinx² + cos x²= 1

$\frac{( \sin {}^{4} (x) + \cos {</p><p>}^{</p><p>4} (x) )(\sin {}^{2} (x) - \cos {}^{2} (x)) + 1 }{ \sin {}^{2} (x) - \cos {</p><p>}^{2} (x) + 1}$

$= \frac{ \sin {}^{2} (x) - \cos {}^{2} (x) + 1 }{ \sin {}^{2} (x) - \cos {}^{2} ( x ) + 1}$

$= 1$

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