Home
Class 12
MATHS
Prove that in a A B C ,sin^3A+sin^2B+si...

Prove that in a ` A B C ,sin^3A+sin^2B+sin^2Clt=9/4dot`

Text Solution

Verified by Experts

`sin^(2)A+sin^(2)B+sin^(2)C`
`=1-cos^(2)A+sin^(2)B+sin^(2)C`
`=1-(cos^(2)A-sin^(2)B)+sin^(2)C`
`=1-cos(A-B)cos(A+B)+1-cos^(2)C`
`=2+cos(A-B)cos C-cos^(2)C`
`le2+cosC-cos^(2)C`. [As `cos(A-B)le1`]
`=2-((cos C-1//2)^(2)-1//4)`
`=9//4-(cos C-1//2)^(2)le9//4`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that in a A B C ,sin^2A+sin^2B+sin^2C<=9/4dot

If A + B + C = 180^@ , then prove that sin 2 A+ sin 2B + sin 2C = 4 sin A sin B sin C

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

If A+B+C = pi , prove that : sin^(2)A +sin^(2)B +sin^(2)C = 2(1+cosAcosBcosC)

Prove that (sin (A - B))/( sin A sin B ) + ( sin (B -C))/( sin B sin C ) + (sin (C - A))/( sin C sin A) =0

If A+B+C=π Prove that in triangle ABC, sin A+sin B+Cle(3sqrt(3))/(2)

If A+B+C=180^0 , prove that : sin^2 A + sin^2 B + sin^2 C =2 (1+cosA cosB cosC)

If (cos^4 A)/(cos^2 B) + (sin^4 A)/(sin^2 B) =1 , Prove that: sin^4 A+sin^4 B=2 sin^2 A sin^2 B

If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 , then prove that (i) sin^4A+sin^4B=2 sin^2Asin^2B (ii) (cos^4B)/(cos^2A)+(sin^4B)/(sin^2A)=1