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given that sinX=2/3, leaving your answer in surd form, calculate tan X -cos X?

Posted in Math, asked by ayodele, 6 years ago. 3942 hits.

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tanx-cosx

sinx/cosx-cosx=>sinx-cos^2x/cosx

we know that sin^2x+cos^2=1=>cos^2x=1-sin^2x

 and also,cosx=root(1-sin^2x)

 sinx-(1-sin^2x)/root(1-sin^2x)

sinx-1+sin^2x/root(1-sin^2x)

we will substitute the values of sinx=2/3

=(2/3)2+2/3-1/root(1-(2/3)^2)

=4/9+2/3-1/root(1-4/9)

=4+6-9/9/root(5)/3

=1/9*3/root(5)

=1/3root(5)

 

Venkat Nagendra Thati
Venkat Nagendra Thati - 6 years ago
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let angle A be x

sinx=opposite/hypotenuse

it means a=2,  c=3 and b=√(3^2-2^2)=√5 →pyth. theorem

therefore, tanx=a/b=2/√5

cosx=b/c=√5/3

tanx-cosx=2/√5-√5/3

getting the LCM and simplifying,

=(6-5)/3√5

=1/(3√5)

or

=√5/15→when you rationalize the denominator

David Owino
David Owino - 6 years ago
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