Question

if 0°≤ theta< 90°, then the least valuenof (sec²theta+cos²theta) is ________.


Steps needed

Answer 1

if cos sq theta is zero,sec theta is undefined

so if cos sq theta is 1, sec sq theta is 1

therefore the least valuenof (sec²theta+cos²theta) is 1+1 i.e. 2

hope this helps you please mark me as brainliest for answering the first

Answer 2

0°≤ θ < 90°

cos²θ + sec²θ

We know that cos θ and sec θ are the reciprocal of each other.

This means that :

• If cos θ is 0 sec θ = infinity ( by limits )
• If sec θ is 0 cos θ = infinity ( by limits )

Clearly cos θ > 0  and sec θ > 0

θ < 90

• When cos θ > 0 but cos θ < 1 so it is a fraction like 1/2
• In such a case cos² θ + sec² θ is more than 2 .
• Apply trial and error and see the value is always more than 2

Only when θ = 90 ,

• cos θ = 1 , so cos² = 1
• sec² θ = 1

So the value of cos²θ + sec²θ = 2

In all other cases it will be more than 2

The minimum value is 2

Hope it helps

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