Question

Which of the following is not equal to
$\frac{cot + cosec - 1}{cot - cosec + 1}$

(A) cosec + cot
(B)
$\frac{cosec + 1}{cot}$

(C)
$\frac{sin}{1 - cos}$

(D)
$\frac{1 + cos}{sin}$
​

Answer 1

Step-by-step explanation:

we have to find the value of cos20° cos100° + cos100° cos140° - cos140° cos200°

solution : cos20° cos100° + cos100° cos140° - cos140° cos200°

= cos100° [ cos20° + cos140° ] - cos140° cos200°

using formula, cosC + cosD = 2cos(C + D)/2 cos(C - D)/2

= cos100° [2cos80° cos60°] - cos140° cos200°

= cos100° [ 2 cos80° × 1/2 ] - cos140° cos200°

= cos100° cos80° - cos140° cos200°

= 1/2 [ 2cos100° cos80° - 2cos140° cos200°]

using formula,

2cosA cosB = cos(A + B) + cos(A - B)

= 1/2 [ cos180° + cos20° - (cos340° + cos60°)]

= 1/2 [ -1 + cos20° - cos340° - 1/2 ]

= 1/2 [ -3/2 + cos20° - cos(360° - 20°)]

= 1/2 [ -3/2 + cos20° - cos20°]

= 1/2 × (-3/2)

= -3/4

Therefore the value of cos20° cos100° + cos100° cos140° - cos140° cos200° = -3/4