1 Determime the value of each or the following Do not use yo

1. Determime the value of each or the following. Do not use your calculstor (a) tan [cos] (bi Ine 2 Verifty the following identities (by tan(2x)-2sinoss 1+cosx sinx 3. Determine the value of (a) cos sin+cos 1 5 (b) sin 2tan 13 4. Solve for , 0

Solution

1) a) tan^-1 ( cos pi )

cos pi = -1

tan^-1 (-1) = - pi/4

therefore, tan^-1 ( cos pi ) = -pi/4

image of 1b and 1c is not clear

2a) sin x / ( 1 + cos x ) = ( 1- cos x ) / sin x

manipulating right hand side

( 1- cos x ) = ( 1 - cos^2 x ) / ( 1 + cos x )

from the identity 1 - cos^2 x = sin^2 x

so we have right side = sin^2 x / ( 1 + cos x ) * sin x

= sin x / ( 1 + cos x )

which is left side

hence proved !

b) tan 2x = ( 2 sin x cos x) / ( cos^2 x - sin^2 x )

manipulating left hand side

2 sin x cos x = sin 2 x

cos^2 x - sin^2 x = cos 2x

so we have right side = sin 2 x / cos 2x

which is equal to tan 2 x

which is left side

hence proved !