Problem 6. (1 point) Fill in the blanks below appropriately to obtain a proof fo

Question

Problem 6.

(1 point) Fill in the blanks below appropriately to obtain a proof for the expression

(1+tan(A)+sec(A))(1+cot(A)csc(A))=2

Proof:

(1+tan(A)+sec(A))(1+cot(A)csc(A))

=1+cot(A)csc(A)+tan(A)+tan(A)cot(A)tan(A)csc(A)+sec(A)+sec(A)cot(A)sec(A)csc(A)=tan(A)csc(A)+tan(Atan(A)csc(A)+sec(A)+sec(A)c

=tan(A)+ _____sec(A)

______+2

=_____ /cos(A)+ ______/ /sin(A)1/(sin(A)/sin(A)_____)+2

=_____ /(sin(A)cos(A) ]+2

=____

/sin(A}cos(A)]+2

=2

Your goal is to fill in the blanks with appropriate formulas to make adjacent expressions equal.
There may be other ways to prove the original identity but this problem requires the correct logic using this approach.

Hint: At each step, look to see which terms might cancel or combine.

Explanation / Answer

(1+tan(A)+sec(A))(1+cot(A)csc(A))=2

Proof:

(1+tan(A)+sec(A))(1+cot(A)csc(A))

=1+cot(A)csc(A)+tan(A)+tan(A)cot(A)tan(A)csc(A)+sec(A)+sec(A)cot(A)sec(A)csc(A)

= tan(A)csc(A)+tan(Atan(A)csc(A)+sec(A)+sec(A)c

= tan(A)+ cot(A) sec(A) csc(A) +2

= sin(A) /cos(A)+ cos(A) /sin(A)1/(sin(A)cos(A)) + 2

=[ sin^(A)+cos^2(A) - 1 /(sin(A)cos(A) ]+2

=[1-1] /sin(A}cos(A)]+2

= 2

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.