sec theta +tan theta =2,then let us determine the value of sec theta - tan theta
Answers
Answer:
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Step-by-step explanation:
sec A+tan A=2
1/cosA+sinA/cosA=2
1+sinA=2cosA
1+2sinA+sin^2A=4cos^2A
1+2sinA+sin^2A=4–4sin^2A
5sin^2A+2sinA-3=0
5 sin^2A+5 sinA-3sinA-3=0
5sinA(sinA+1)-3(sinA+1)=0
(sinA+1)(5sinA-3)=0
sinA=-1 , 3/5
Now sinA+cosA=sinA+(1-sin^2A)^1/2 put sinA =-1 , 3/5
=-1+[1-(-1)^2]^1/2 , 3/5+[1-(3/5)^2]^1/2
=-1+0 , 3/5+4/5
= -1 , 7/5 , Answer
Answer:
As you can see in the picture I've used one trigonometric identity and one algebraic identity to solve the question.
The identity can be written in the form of (a-b)(a+b)=a^2 - b^2
Putting the given value of 2 in the equation we get a linear equations, which we add to the second equation.
It directly gives us the value of tan(theta)
I won't suggest using the inverse methods because tan(theta) can approach to many different values.
If you need help on any question feel free to ask me.
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Best of Luck!
Step-by-step explanation:
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