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secondary 4 | A Maths
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Hello everyone !!!!!!
Please help me with the
“show 5tanA=2cotB” and (i) tan(A+B) :)
Thanks so much:)
Date Posted: 4 years ago
Views: 349
cos(A-B) = cosAcosB+sinAsinB
cos(A+B) = cosAcosB-sinAsinB
Given: cos(A-B)/cos(A+B) = 7/3
=> 3cos(A-B) = 7cos(A+B)
=> 3cosAcosB+3sinAsinB = 7cosAcosB-7sinAsinB
=> 10sinAsinB = 4cosAcosB
=> 5sinAsinB = 2cosAcosB
divide all thru' by cosAcosB,
=> 5tanAtanB = 2
=> 5tanA = 2cotB (shown)
...
cos(A+B) = cosAcosB-sinAsinB
Given: cos(A-B)/cos(A+B) = 7/3
=> 3cos(A-B) = 7cos(A+B)
=> 3cosAcosB+3sinAsinB = 7cosAcosB-7sinAsinB
=> 10sinAsinB = 4cosAcosB
=> 5sinAsinB = 2cosAcosB
divide all thru' by cosAcosB,
=> 5tanAtanB = 2
=> 5tanA = 2cotB (shown)
...
See 2 Answers
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Good evening Sonia! Here is what we can do for the first part. I will send the remaining parts at a later time.
Date Posted:
4 years ago
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Hi Sonia! Here are the remaining parts for the question.
Part 1 requires you to use the formula from the list. Note that we cannot write tan (A + B) as tan A + tan B, unlike in algebra where 5 (A + B) = 5A + 5B.
Part 2 requires you to draw out the triangle for reference. Fortunately angle A is acute, so all three trigonometric ratios (sin, cos, tan) have positive values.
For part 3, we cannot tell by one look whether 2A is acute or obtuse, since 0 < A < 90 means 0 < 2A < 180 and cos 2A can be positive or negative. Hence, we cannot draw out the triangle for angle 2A, and instead, we must use the double angle formula to break the angle into an equivalent form involving angle A.
Part 1 requires you to use the formula from the list. Note that we cannot write tan (A + B) as tan A + tan B, unlike in algebra where 5 (A + B) = 5A + 5B.
Part 2 requires you to draw out the triangle for reference. Fortunately angle A is acute, so all three trigonometric ratios (sin, cos, tan) have positive values.
For part 3, we cannot tell by one look whether 2A is acute or obtuse, since 0 < A < 90 means 0 < 2A < 180 and cos 2A can be positive or negative. Hence, we cannot draw out the triangle for angle 2A, and instead, we must use the double angle formula to break the angle into an equivalent form involving angle A.
Date Posted:
4 years ago
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