Home
Class 12
MATHS
Show that 1/(sin 10^@) - sqrt3/(cos 10^@...

Show that `1/(sin 10^@) - sqrt3/(cos 10^@) = 4`

Text Solution

Verified by Experts

`(1)/(sin 10^(@))-(sqrt(3))/(cos10^(@))=(cos10^(@)-sqrt(3)sin10^(@))/(sin10^(@)cos10^(@))`
`=4xx((1)/(2)cos10^(@)-cos30^(@)sin 10^(@))/(sin20^(@))`
`=4xx(sin20^(@))/(sin 20^(@))=4`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.5|6 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.6|5 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.3|13 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos
  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

(1)/(cos 80^(@)) - (sqrt(3))/(sin 80^(@)) =

1/(cos80^o) -sqrt3/(sin80^o ) =

Show that sin ( 40 ^@ +x ) cos ( 10^@ +x ) - cos ( 40 ^@ +x ) sin (10 ^@ +x )=1/2

(1) /( cos 80^@ ) - ( sqrt(3))/( sin 80 ^@) =

(cos 10^(@) - sin 10^(@))/(cos 10^(@) + sin 10^(@)) is

Prove that (cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0

Show that (sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x) = tan 2x

Show that ( 2 + i sqrt(3))^(10) - (2 - i sqrt(3))^(10) is purely imaginary.

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 ...

    Text Solution

    |

  2. (sin ^2 3A )/( sin ^2 A ) -( cos^2 3A )/(cos ^2 A ) is

    Text Solution

    |

  3. Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/...

    Text Solution

    |

  4. If in an isosceles triangle with base 'a', vertical angle 20^@ and lat...

    Text Solution

    |

  5. In DeltaABC, a = 3, b = 4 and c = 5, then value of sinA + sin2B + sin...

    Text Solution

    |

  6. If cos A = 3/4 then sin ""(A) /(2 ) . Sin 5 (A)/(2) is

    Text Solution

    |

  7. Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@...

    Text Solution

    |

  8. If theta is an acute angle and sin((theta)/(2))=sqrt((x-1)/(2x)) ,then...

    Text Solution

    |

  9. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

    Text Solution

    |

  10. Let a=(pi)/(7), then (a) show that sin^(2)3a-sin^(2)a=sin2asin3a (...

    Text Solution

    |

  11. Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

    Text Solution

    |

  12. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

    Text Solution

    |

  13. If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value...

    Text Solution

    |

  14. tantheta+tan(6 0^0+theta)+tan(12 0^0+theta)=3tan3theta

    Text Solution

    |

  15. If A=110^(@), then prove that (1+sqrt(1+tan^(2)2A))/(tan2A)=-tan A.

    Text Solution

    |

  16. If alpha and beta are the two different roots of equations alpha cos t...

    Text Solution

    |

  17. If tan beta=cos theta tan alpha, then prove that tan^(2)""(theta)/(2)=...

    Text Solution

    |

  18. If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta...

    Text Solution

    |

  19. If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta),prove that ta...

    Text Solution

    |

  20. If tan theta tan phi=sqrt((a-b)/(a+b)), prove that a-bcos 2theta)(a-...

    Text Solution

    |