Question

Given
\cos(\alpha)=\frac{\sqrt{17}}{9}
for 0<\alpha<\pi/2.

Also given
\cos(\beta)=\frac{\sqrt{7}}{4}
and 0<\beta<\pi/2.

Use sum and difference formulas to find the following:

Note: You are not allowed to use decimals in your answer.

\tan(\alpha + \beta)=

Answer 1

can you retype your answer? its so hard to understand

Answer 2

retype the question i mean

Answer 3

\(\cos(\alpha)=\frac{\sqrt{17}}{9}\)
for \(0<\alpha<\pi/2\).

Also given
\(\cos(\beta)=\frac{\sqrt{7}}{4}\)
and \(0<\beta<\pi/2\).

\(\tan(\alpha + \beta)=\)

Retyped the equation bit.

Answer 4

\[\cos (\alpha)=\frac{ \sqrt{17} }{ 9 } for 0<\alpha<\frac{ \pi }{ 2}, also given \cos (\beta)=\frac{ \sqrt{7} }{ 4} and 0<\beta<\frac{ \pi }{ 2 }\]

Answer 5

\[\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)\]\[=\cos(\alpha)\cos(\beta)-\sqrt{1-\cos^2(\alpha)}\sqrt{1-\cos^2(\beta)}\]Use that to get cos(a+b)

\[\tan(\alpha+\beta)=\frac{ \sin(\alpha+\beta) }{ \cos(\alpha+\beta) }=\frac{\sqrt{1-\cos^2(\alpha+\beta)}}{\cos(\alpha+\beta)}\] You work out the details! :)

Answer 6

ok. thank you