Home
Class 10
MATHS
If s in A=3/4 , calculate cos A an...

If `s in A=3/4` , calculate cos A and tan A.

Text Solution

Verified by Experts


`sinA=(3)/(4)` Construct `DeltaABC` , right - angled at B such that
`BC=3kandAC=4k`
In `DeltaABC`,
From Pythagoras theorem
`AB^(2)=AC^(2)-BC^(2)=(4k)^(2)-(3k)^(2)=16k^(2)=9k^(2)=7k^(2)`
`rArrAB=sqrt(7)k`
Now , `cosA=(AB)/(AC)=(sqrt(2)k)/(4k)=(sqrt7)/(4)`
`tan A=(BC)/(AB)=(3k)/(sqrt(7)k)=(3)/(sqrt(7))`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 8a|20 Videos
  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 8 B|22 Videos
  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos
  • CONSTRUCTIONS

    NAGEEN PRAKASHAN|Exercise PROBLEMS FROM NCERT/ EXEMPLAR|10 Videos
  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

If sin A=(3)/(4), calculate cos A and tan A

In a Delta ABC, if cos A cos B cos C=(1)/(3) then value of,tan A tan B+tan B tan C+tan C tan A is

If 3 tan A = 4, then the value of (3 sin A + 2 cos A)/(3 sin A - 2 cos A) is:

If tan A = (3)/(4) , find the value of (1)/( sin A) + (1)/( cos A)

If A lies in the third quadrant and tan A=(4)/(3) then find the value of sin A+cos A

If 3tan A=4 then find sin A and cos A

In Delta ABC If cos A cos B cos C=(1)/(3) then tan A tan B+tan B tan C+tan C tan A=

If sin theta = 3/4 and tan theta =9/2, then cos theta is

If tan A=(3)/(4) then find the value of sin A*cos A

NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. If sqrt(3)tantheta=1 then find value of sin^2theta-cos^2theta

    Text Solution

    |

  2. given : 15 cotA = 8 find sinA and secA

    Text Solution

    |

  3. If s in A=3/4 , calculate cos A and tan A.

    Text Solution

    |

  4. If angleA and angleB are acute angles such that cos A= cos B, then sho...

    Text Solution

    |

  5. (cos45)/(sec30+cosec30)

    Text Solution

    |

  6. Choose the correct option and justify your choice : (i) (2tan30o)/...

    Text Solution

    |

  7. If tan(A+B)=sqrt(3) and t a n(A B)=1/(sqrt(3)); 0o<A+Blt=90o;""...

    Text Solution

    |

  8. In DeltaA B C , right-angled at B, A B"\ "="\ "5"\ "c m and /A C B=30...

    Text Solution

    |

  9. In P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine ...

    Text Solution

    |

  10. Prove that : sqrt((1-cos^(2)theta)sec^(2)theta)=tantheta

    Text Solution

    |

  11. Prove (tantheta+2)(2tantheta+1)=5tantheta+2sec^2theta.

    Text Solution

    |

  12. If cosA+cos^(2)A=1, then prove that sin^(2)A+sin^(4)A=1.

    Text Solution

    |

  13. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

    Text Solution

    |

  14. Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

    Text Solution

    |

  15. Prove that : (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα...

    Text Solution

    |

  16. Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"t...

    Text Solution

    |

  17. If 2sin^(2)theta-cos^(2)theta=2, then find the value of theta.

    Text Solution

    |

  18. if tantheta+sectheta=l then prove that tantheta=(l^2+1)/(2l)

    Text Solution

    |

  19. If asintheta+bcostheta=c then prove that acostheta-bsintheta=sqrt(a^2+...

    Text Solution

    |

  20. If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(...

    Text Solution

    |