minimum value of 4tan²∅+3cos²∅
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Let a= 4tan^2 theta
And let b= 9cot^2theta
Then, according to AM-GM inequality
STEP 1:(4tan^2 theta+9cot^2theta)/2≥√(4tan^2theta×9tan^2theta)
STEP 2:(4tan^2theta+9cot^2theta)/2≥2×3×tan theta×cot theta
4tan^2theta+9cot^2theta≥12
Hence, the minimum value is 12
Hope it will help you.
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And let b= 9cot^2theta
Then, according to AM-GM inequality
STEP 1:(4tan^2 theta+9cot^2theta)/2≥√(4tan^2theta×9tan^2theta)
STEP 2:(4tan^2theta+9cot^2theta)/2≥2×3×tan theta×cot theta
4tan^2theta+9cot^2theta≥12
Hence, the minimum value is 12
Hope it will help you.
Please mark it as a BRAINLIEST one.
☺☺☺☺☺
priyanka89621:
thnxx
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