Question

${sin}^{2} a \times { \tan}^{2} a + \cos^{2} a = \sec^{2}a - {2 \sin }^{2} a$
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Answer 1

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Answer 2

step by step explanation

step by step explanationwe have given that

step by step explanationwe have given that sin²a .tan²a+cos²a=sec²a-2sin²a

(changin tan a & COS a in terms of sine and cos )

=>sin²a.sin²a/cos²a+cos²a=1/cos²a -2sin²a

=> sin^4a/cos²a + cos²a=1-2sin²acos²a/cos²a

(on both side we have cos²a as denominator so they will cancel out each other )

sin^4a + cos^4a = 1-2sin²acos²a

sin^4a +cos^4a + 2sin²acos²a = 1

(by using a²+b²+2ab =(a+b)²)

(sin²a+cos²a)²=1

1²=1

1=1

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