# Trigonometry Help! How do I simplify sec^2/(tan+cot)?

Ok so I have a major assignment due Monday, and I have 20 out of the 26 questions done. I really need help simplifying the following.

Simplify

A) sec^2/(tan+cot)

B) ((1+sin)/cos)+ (cos/(1+sin))

C) (tan^2/ (1+sec)) cos*sec.

I realize for C that cos and sec reduce to 1 as

Relevance
• Anonymous
9 years ago

A) sec^2/(tan+cot)

Solution:

(1/cos^2) / ((sin/cos)+(cos/sin))

(1/cos^2) / ((sin^2 +cos^2)/(cos.sin))

(1/cos^2) / (1 /(cos.sin)) Since sin^2 + cos^ =1

(1/cos^2) * (cos.sin)

(sin/cos)

B) ((1+sin)/cos)+ (cos/(1+sin))

Taking LCM

{(1+sin)^2 + cos^2} / {cos(1+sin)}

Expanding (1+sin)^2 through (a+b)^2 formula

(1+2sin+sin^2+cos^2) / {cos(1+sin)}

(1+2sin+1) / {cos(1+sin)} Since sin^2 + cos^ =1

(2+2sin) / {cos(1+sin)}

2(1+sin) / {cos(1+sin)}

2/cos

C) (tan^2/ (1+sec)) cos*sec.

Since cos*sec=1

(tan^2)/ (1+sec)

(sec^2-1)/ (1+sec) since 1+tan^2=sec^2

{(sec+1)(sec-1)} / (1+sec) Expanding (sec^2-1) by (a^2 - b^2) formula