Establish the identity sin theta tan theta cos theta sec t

Establish the identity: sin theta tan theta + cos theta = sec theta Find all solutions of the equation 2sin^2 theta + 3sin theta + l = 0 in the interval [0, 2 pi). Find all solutions of the equation sin 2 theta = sin theta in the interval [0, 2 pi). RECALL sin2 theta = 2sin theta cos theta The angle of elevation from a stone on level ground to the top of a 28-foot tall tree is 57 degree. Find the distance from the stone to the base of the tree.

Solution

9)sintan +cos

=sin(sin_/cos) +cos

=(sin²_/cos) +cos

=(sin²+cos²)_/cos

=1_/cos

=sec

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10) 2sin² +3sin+1=0

2sin²+2sin+sin+1=0

2sin(sin+1)+1(sin+1)=0

(sin+1)(2sin+1)=

sin =-1, sin =-1_/2

=3/2 ,=7/6, 11/6

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11)sin2=sin

2sincos=sin

2sincos-sin=0

sin(2cos -1) =0

sin=0, cos=1/2

=0, ,=/3,5/3 ,

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12)let distance from stone to base of tree =x

tan57^o=28/x

x=28/tan57^o

x=18.18