Question

(1-cos^2 theta)sec^2 theta=tan^2 theta​

Answer 1

Step-by-step explanation:

LHS

We know the identity that

• Sin theta = 1 - cos² theta

So we can put Sin theta in the bracket as:-

sin² theta × sec² theta

Now we also know that

• Sec theta = 1/ cos theta

So putting cos ² theta in place of sec ² theta

Sin² theta × 1/ cos² theta

Now we know that

• tan theta = sin theta / cos theta

So we got tan² theta in LHS.

RHS

Already Tan² theta given

So,

LHS = RHS

Hence Proved.

Some Identities

• Sin²0 = 1 - cos²0
• 1 + tan²0= sec²0
• 1 + cot²0= cosec²0
• Sin0= cos0/cot0
• Tan0 = sin0/cos0
• Cos0= cot0/cosec0
• cosec0= sec0/tan0
• sec0= tan0/sin0
• cot0= cosec0/sec0
• Where 0 is theta

Answer 2

Answer:

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GIVEN : (1-cos^2 theta)sec^2 theta=tan^2 theta

➡ (1- cos^2 theta) sec ^2 theta

• 1 - cos ^2 theta = sin ^2 theta

Substitute it, we get....

➡ (sin ^2 theta) (sec^2 theta)

• sec^2 theta = 1 / cos ^2 theta

Substitute it, we get.....

➡ (sin ^2 theta) ( 1 / cos ^2 theta)

➡ sin ^2 theta/ cos ^2 theta

• sin ^2 theta/ cos ^2 theta = tan^2 theta

➡ tan ^2 theta

THEREFORE IT IS PROVED...

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Step-by-step explanation:

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