Question

sin theta + cos theta divided by sin theta minus cos theta + sin theta minus cos theta divided by sin theta + cos theta is equal to 2 secant squared theta divided by tan squared theta minus one



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Answer 1

Answer:

The angles at which the relative error exceeds 1% are as follows: tan θ ≈ θ at about 0.176 radians (10°). sin θ ≈ θ at about 0.244 radians (14°). cos θ ≈ 1 − θ22 at about 0.664 radians (38°

Step-by-step explanation:

Answer 2

Step-by-step explanation:

LHS=

(sin theta+cos theta) / ( sin theta - cos theta)

+( sin theta+ cos theta) / ( sin theta+ cos theta)

= [ (sin theta+ cos theta)²+(sin theta- cos theta)²]

divided by (sin²theta- cos² theta)

= (1+ sin2theta+1-sin2theta) / ( 2sin²theta-1)

= 2 / (2sin²theta -1)

multipliying and dividing by sec² theta

= 2sec²theta / (2 sin² theta-1) sec² theta

= 2 sec² theta / ( 2 tan²theta- sec²theta)

= 2sec²theta/ [ tan²theta-(sec²theta-tan²theta)]

= 2sec²theta /( tan²theta -1)

= RHS

PROVED

formula used

(1) sin²theta+ cos²theta = 1

(2) 2 sin theta cos theta = sin2 theta

(3) (a+b)(a-b) = a²-b²

(4) sec²theta- tan²theta =1

(5) sin theta.sec theta = tan theta

hope this helps you