Answer:
[tex]\text{a. }\dfrac{a}{\sqrt{1-a^2}}[/tex]
[tex]\text{b. }\sqrt{1-a^2}[/tex]
Formula used:
[tex]1.\ \sin^2x+\cos^2x=1\\[/tex]
[tex]\Rightarrow\cos^2x=1-\sin^2x\\[/tex]
[tex]\Rightarrow\cos x=\sqrt{1-\sin^2 x}[/tex]
[tex]2.\ \tan x=\dfrac{\sin x}{\cos x}[/tex]
[tex]\text{3. }\sin(90+\theta)=\cos\theta[/tex]
Step-by-step explanation:
[tex]\text{a. Solution: }\\\\\tan 17=\dfrac{\sin 17}{\cos 17}[/tex]
[tex]\text{or, }\tan 17=\dfrac{a}{\sqrt{1-\sin^2 17}}[/tex]
[tex]\text{or, }\tan 17=\dfrac{a}{\sqrt{1-a^2}}[/tex]
[tex]\text{b. Solution:}\\\sin 107=\sin (90+17)=\cos 17=\sqrt{1-\sin^2 17}=\sqrt{1-a^2}[/tex]
