Question

[sec²θ-tan²θ+0] [sin²θ-cos²θ-1]

[cot²θ-cosec²θ+1]. [0-1+0]​

Answer 1

Step-by-step explanation:

Ans:

sin2θ + cos2θ = 1

sec2θ = 1 + tan2θ

cosec2θ = 1 + cot2θ

Using these identities we can simplify the given equation as

sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ

= (sin²θ + cos²θ) + (sec²θ + tan²θ) + (cosec²θ + cot²θ)

= 1 + 1 + 2tan²θ + 1 + 2cot²θ

= 3 + 2(tan²θ + cot²θ)

Now, using AM-GM inequality we can say

min(tan²θ + cot²θ) = 2

So, min(3 + 2(tan²θ + cot²θ)) = 3 + 2*2 = 7