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enyata [817]
3 years ago
9

Which expression is equivalent to sec^2x − 1? a. cot2x b. tan2x c. csc2x d. cos2x

Mathematics
2 answers:
Nesterboy [21]3 years ago
4 0
Sec^2 x - 1 = tan^2x

Proof:
Sec^2x = 1+ tan^2x

1/cos^2x = 1 + sin^2x/cos^2x

<span>1/cos^2x - sin^2x/cos^2x = 1
</span>Using common denominator:
(1-sin^2x)/cos^2x = 1
sin^2x + cos^2 x = 1
cos^2 x = 1 - sin^2x
Substituting : 
cos^2x/<span>cos^2x = 1
</span>1 = 1
Left hand side = right hand side 
Artyom0805 [142]3 years ago
4 0

Answer:

option B tan²x

Step-by-step explanation:

We have to simplify the expression given as ( sec^{2}x-1 )

Since sec x = \frac{1}{cosx}

so ( \frac{1}{cosx} )² - 1 = \frac{1}{cos^{2} x} - 1

=\frac{1-cos^{2}x }{cos^{2}x}

= \frac{sin^{2}x }{cos^{2}x}

= tan²x

Therefore, option B tan²x is the answer.

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