Home
Class 12
MATHS
If (1+sinA)(1+sinB)(1+sinC)=(1-sin-A) ...

If `(1+sinA)(1+sinB)(1+sinC)=(1-sin-A)`
`(1-sinB)(1-sinC)," then prove that "(1+sinA)`
`(1-sinB)(1-sinC)=pmcosA.cosB.cosC`.

Text Solution

Verified by Experts

Multiplying both sides by `(1-sinA)(1-sinB)(1-sinC)`, we get
`(1-sin^2A)(1-sin^2B)(1-sin^2C)`
`= (1-sinA)^2(1-sinB)^2(1-sinC)^2`
`rArr (1-sinA)(1-sinB)(1-sinC)`
`=pmcosAcosBcosC`
Similrly,`(1+sinA)(1+sinB)(1+sinC)`
`=pmcoAcosBcosC`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.3|4 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.4|4 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.1|8 Videos
  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If (1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC) , then prove that each side is equal to +-cosAcosBcosC .

If A+B+C=180 , prove that: sinA+sinB+sinC=4cosA/2cosB/2cosC/2

In DeltaABC , prove that: sinA+sinB-sinC=4sinA/2sinB/2cosC/2

If A+B+C=pi , prove that : sinA+sinB+sinC= 4cos( A/2 )cos( B/2) cos(C/2)

Prove that (sinA + sinB)/(cosA + cosB)= tan((A+B)/2)

If in a !ABC , (sinA+sinB+sinC)(sinA+sinB-sinC)=3sinAsinB then

In a DeltaABC, sin A sinB sinC is

If (sinA+sinB+sinC)^(2)=sin^(2)A+sin^(2)B+sin^(2)C , then which one is true?

If sinA=sinB and cosA=cosB , then prove that sin. (A-B)/(2)=0 .