Question

sec^4A(1-sin^4A)-2tan²A=1 prove this no spam​

Answer 1

Answer:

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Answer 2

Answer:

Consider the L.H.S,

=sec

4

A(1−sin

4

A)−2tan

2

A

=sec

4

A−sec

4

Asin

4

A−2tan

2

A

=sec

4

A−

cos

4

A

sin

4

A

−2tan

2

A

=sec

4

A−tan

4

A−2tan

2

A

=[(sec

2

A)

2

−(tan

2

A)

2

]−2tan

2

A

=[(sec

2

A)−(tan

2

A)][(sec

2

A)+(tan

2

A)]−2tan

2

A

We know that

sec

2

A−tan

2

A=1

Therefore,

=sec

2

A+tan

2

A−2tan

2

A

=sec

2

A−tan

2

A

=1

Hence, proved