Question

in a triangle sec A (cosB cosC -sinB sinC) is equal to​

Answer 1

Answer:

In a triangle ABC,

A+B+C = 180°

i.e. B+ C= 180 - A ------------(1)

now, secA ( cos B cos C - sin B sin C) ----(2)

as we know that

cos (x + y) = cos x cos y - sin x sin y

similarly, cos B cos C - sin B sin C = cos ( B+C)

put in equation (2)

sec A ( cos B cos C - sin B sin C)

Sec A [ cos ( B + C ) ]

put the value of B+ C from equation (2)

sec A[ cos ( 180 - A)]

sec A [ cos (-A)] because cos (180 - A) = cos (-A)

sec A ( cos A)

=1