Search
Ask a question
-1

Use C to denote cos(x), and express 1+tan^2(x)=______ in terms of C. Similarly, express (1-sinx)(1+sinx)=____ in terms of C.

Hint: For the first part use the definition of the tangent function. For the second part use the third binomial formula:
(a+b)(a-b)=a^2-b^2
 
Can you please show clear steps on how you got this? I want to master this as soon as possible.

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (6 lesson ratings) (6)
0
1+tan2(x)=sec2(x) is a trig identity
sec(x)=1/cos(x) is a trig identity
substitute
1+tan2(x)=(1/cos[x])2
1+tan2(x)=1/cos2(x)
 
sin2(x)+cos2(x)=1 is a trig identity
subtract sin2(x) from both sides to get...
cos2(x)=1-sin2(x)
(1-sinx)(1+sinx)=1-sinx+sinx-sin2(x)
(1-sinx)(1+sinx)=1-sin2(x)
1-sin2(x)=cos2(x) from the above identity

Comments

1+tan^2(x)=
1+sin^2(x)/cos^2(x)=
[cos^2(x)+sin^2(x)]/cos^2(x)=
1/cos^2(x) if you need to use the tan function only
 
It's saying that it is incorrect. I'm pretty sure the answers are correct, but it's saying the function 'cos' is missing its inputs. Weird.