Question

if sin (90° - theta) cos theta = 1 and theta is an acute angle then theta____​

Answer 1

SOLUTION

TO FILL IN THE BLANK

If sin (90° - θ) cos θ = 1 and θ is an acute angle then θ = ____

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric identity that

$\displaystyle \sf{ \sin ( {90}^{ \circ} - \theta ) = \cos \theta }$

EVALUATION

Here it is given that

$\displaystyle \sf{ \sin ( {90}^{ \circ} - \theta ) \cos \theta = 1 }$

We now use the formula

$\boxed{ \: \: \displaystyle \sf{ \sin ( {90}^{ \circ} - \theta ) = \cos \theta } \: \: }$

Now we have

$\displaystyle \sf{ \sin ( {90}^{ \circ} - \theta ) \cos \theta = 1 }$

$\displaystyle \sf{ \implies \cos \theta \cos \theta = 1 }$

$\displaystyle \sf{ \implies {\cos}^{2} \theta = 1 }$

$\displaystyle \sf{ \implies \cos \theta = 1 } \: \: \: (\because \: \theta \: is \: acute)$

$\displaystyle \sf{ \implies \cos \theta = \cos {0}^{ \circ} }$

$\displaystyle \sf{ \implies \theta = {0}^{ \circ} }$

FINAL ANSWER

If sin (90° - θ) cos θ = 1 and θ is an acute angle then θ = 0°

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Answer 2

Step-by-step explanation:

S

$\sin(90^o \: - theta) \cos(theta) = 1 \\ \cos^{2} = 1 \\ \cos(theta) = 1 \\ \cos(theta) = \cos(0) \\ theta = 0^{0}$

$theta$