Question

prove 1-tanh^2x = 1/cosh^2x

Answer 1

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There's a slight mistake in your question. It should be 1+tan²x not 1-tan²x. Please check it.

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

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Answer 2

Answer:

Step-by-step explanation:

1-tan²x = 1/ cos²x

Consider L.H.S = 1-tan²x

1-tan²x = sec²x. (It's an identity)

sec²x = 1/cos²x

Hence Proved...