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REY [17]
3 years ago
9

Verify the identity​

Mathematics
1 answer:
Oxana [17]3 years ago
3 0

Answer:

see below

Step-by-step explanation:

sin x                                 1

-------------------              = -----------

sec^2 x - tan ^2 x               csc x

Sec = 1/cos   and tan = sin/cos

sin x                                         1

-------------------                     = -----------

1/ cos ^2 x -sin^2/cos ^2 x       csc x

Factor the denominator

sin x                                         1

-------------------                     = -----------

(1-sin^2 x)/ cos ^2 x                csc x

We know that 1 - sin^2 x = cos ^2

sin x                                         1

-------------------                     = -----------

(cos^2 x)/ cos ^2 x                csc x

sin x                                         1

-------------------                     = -----------

1                                               csc x

Multiply the top and bottom of the left hand side by 1/ sin x

sin x  * 1/ sin x                              1

-------------------                     = -----------

1     * 1 sin x                             csc x

1                                                1

-------------------                     = -----------

       1 sin x                             csc x

We know that 1/sin x = csc

1                              1

---------               = -----------

csc (x)                   csc x

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