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A quadrilateral ABCD is inscribed in a circle as shown in the figure.
Based on the above data, answer the following question.
Q. The value of y is .............
A quadrilateral ABCD is inscribed in a circle as shown in the figure.
Based on the above data, answer the following question.
Q. cos A + cos B + cos C + cos D = ...........
= cos A + cos B + cos(180° – A) + cos(180° – B)
= cos A + cos B – cos A – cos B = 0
A quadrilateral ABCD is inscribed in a circle as shown in the figure.
Based on the above data, answer the following question.
Q. cos(A + B + C + D) = .............
A + B + C + D = 360°
cos(A + B + C + D) = cos 360° = 1
A quadrilateral ABCD is inscribed in a circle as shown in the figure.
Based on the above data, answer the following question.
Q. sin (B + D) = ..............
B + D = 180° (opposite angles are supplementary)
∴ sin(B + D) = sin 180° = 0
A quadrilateral ABCD is inscribed in a circle as shown in the figure.
Based on the above data, answer the following question.
Q. The value of x is ..............
⇒  4x + 4y + 20 = 180°
 4x + 4y = 160°
x  y =  40° ...(i)
B + D = 180°
⇒ 3y  5  7x + 5 = 180°
 7x + 3y = 180° ...(ii)
Solving (i) and (ii), x = –15°
A compound angle is an angle which can be expressed as the sum or difference of two standard angles.
Based on the above data, answer the following question.
Q. The value of tan 75° is = .............
=
=
= 2 + √3 (after rationalising denominator)
A compound angle is an angle which can be expressed as the sum or difference of two standard angles.
Based on the above data, answer the following question.
Q. sin(A + B).sin(A  B) = .............
= (sin A. cos B + cos A. sin B)(sin A. cos B  cos A. sin B)
= (sin A. cos B)^{2}  (cos A. sin B)^{2}
= sin^{2} A. cos^{2} B  cos^{2} A. sin^{2} B
= sin^{2} A (1  sin^{2} B)  (1  sin^{2} A) sin2 B
= sin^{2} A  sin^{2} A. sin^{2} B  sin^{2} B + sin^{2} A. sin^{2} B
= sin^{2} A  sin^{2} B
A compound angle is an angle which can be expressed as the sum or difference of two standard angles.
Based on the above data, answer the following question.
Q. The value of cos 75° is ..............
= cos 30°.cos 45° – sin 30°.sin 45°
=
=
A compound angle is an angle which can be expressed as the sum or difference of two standard angles.
Based on the above data, answer the following question.
Q. 1 + cos 2A = ............
= cos A. cos A – sin A. sin A
= cos^{2} A – sin2 A
= cos^{2} A – (1 – cos^{2} A)
= 2 cos^{2} A – 1
∴ 1 + cos 2 A = 2 cos^{2} A
A compound angle is an angle which can be expressed as the sum or difference of two standard angles.
Based on the above data, answer the following question.
Q. The value of sin 75° is ..............
= sin 30°.cos 45° + cos 30°.sin 45°
=
=
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