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Consider the following two statements :
Statement p :
The value of \sin 120^{\circ} can be derived by taking \theta = 240^{\circ} in the equation 2\sin \frac{\theta }{2}=\sqrt{1+\sin \theta }-\sqrt{1-\sin \theta } 

Statement q :
The angles A, B, C and D of any quadrilateral ABCD satisfy the equation \cos \left ( \frac{1}{2}\left ( A+C \right ) \right )+\cos \left ( \frac{1}{2}\left ( B+D \right ) \right )=0

Then the truth values of p and q are respectively :

  • Option 1)

    F,T

  • Option 2)

    T,F

  • Option 3)

    T,T

  • Option 4)

    F,F

 

Answers (1)

best_answer

\sin 120^{\circ}=\frac{\sqrt{3}}{2}\: \Rightarrow \: 2\sin 120^{\circ}=\sqrt{3}

\sqrt{1+\sin 240^{\circ}}-\sqrt{1-\sin 240^{\circ}}=\sqrt{\frac{1-\sqrt{3}}{2}}-\sqrt{\frac{1+\sqrt{3}}{2}}

Sq \frac{A+C}{2}+\frac{B+C}{2}=\pi =\cos \frac{\left ( A+C \right )}{2}\cos \frac{\left ( B-C \right )}{2}

p is False, q is True


Option 1)

F,T

Option 2)

T,F

Option 3)

T,T

Option 4)

F,F

Posted by

Himanshu

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