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If a^2+b^2+2a bcostheta=1,c^2+d^2+2c dco...

If `a^2+b^2+2a bcostheta=1,c^2+d^2+2c dcostheta=1` and `a c+b d+(a d+b c)costheta=0,` then prove that `a^2+c^2=cos e c^2theta`

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If a^2+b^2+2a bcostheta=1,c^2+a^2+2c dcostheta=1 and a c+b d+(a d+b c)costheta=0, then prove that a^2+c^2=cos e c^2theta

The value of sqrt((1+costheta)/(1-costheta)) is (a) cottheta-cos e c\ theta (b) cos e c\ theta+cottheta (c) cos e c^2theta+cot^2theta (d) (cottheta+cos e c\ theta)^2

If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2)costhetab a(1-costheta)c a(1-costheta)a b(1-costheta)b^2+(c^2+a^2)costhetac b(1-costheta)a c(1-costheta)b c(1-costheta)c^2+(a^2+b^2)costheta| simplifies to cos^2theta

If A D is the median of A B C , using vectors, prove that A B^2+A C^2=2(A D^2+C D^2)dot

If acottheta+b"c o s e c"theta=p and bcottheta+a"c o s e c"theta=q , then p^2-q^2= (a) a^2-b^2 (b) b^2-a^2 (c) a^2+b^2 (d) b-a

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : cos theta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

c(1+cos2theta)= (A) c 2sin^2theta (B) c2cos^2theta (C) c2tan^2theta (D) none of these

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that ("a c o s"A+b cosB+c cosC)/(a+b+c)=r/Rdot

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  2. Find the number of solution of the equation 1+e^(cot^2x)=sqrt(2|sinx|-...

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  3. If a^2+b^2+2a bcostheta=1,c^2+d^2+2c dcostheta=1 and a c+b d+(a d+b c)...

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  4. If r1=r2+r3+r prove that the triangle is right angled .

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  5. Find the number of solution of theta in [0,2pi] satisfying the equati...

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  6. Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-bet...

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  7. Let A=sinx+cosxdot Then find the value of sin^4x+cos^4x in terms of Ad...

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  8. ABC is an acute angled triangle with circumcenter O and orthocentre H....

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  9. If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of t...

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  10. In quadrilateral A B C D , if sin((A+B)/2)cos((A-B)/2)+"sin"((C+D)/2)c...

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  11. Find the range of y=sin^3x-6sin^2x+11sinx-6.

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  12. A ladder rest against a wall making an angle alpha with the horizontal...

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  13. Let ABC be an acute angled triangle whose orthocentre is at H. If a...

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  14. The most general value for which tantheta=-1 and costheta=1/(sqrt(2)) ...

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  15. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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  16. Prove that: cos18^0-sin18^0 = sqrt(2)sin27^0

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  17. In a acute angled triangle ABC, proint D, E and F are the feet of the ...

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  18. The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi...

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  19. Which of the following is correct ? (a) sin1^@>sin1 (b) sin1^@<sin1 (c...

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  20. Prove that: (sin5A-sin3A)/(cos5A+cos3A)=tanA (2)(sinA+sin3A)/(cosA+c...

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