Question

If tan 35° tan 55° = sin theta , then the lowest positive value of theta will be

Answer 1

the lowest positive value of theta is zero.

hope this helps you

Answer 2

Answer:

Lowest value of $\theta$ is 90°

Step-by-step explanation:

Given,

$\tan( {35}^{o} ) \times \tan( {55}^{o} ) = \sin( \theta) \\ \tan( {90}^{o} - {55}^{o} ) \times \tan( {55}^{o} ) = \sin( \theta) \\ \cot( {55}^{o} ) \times \tan( {55}^{o} ) = \sin( \theta) \\ \frac{1}{ \tan( {55}^{o} ) } \times \tan( {55}^{o} ) = \sin( \theta) \\ \sin( \theta) = 1 \\ \sin( \theta) = \sin( {90}^{o} ) \\ \theta = {90}^{o}$

Therefore lowest positive value of $\theta$ is 90°.

Here applied formula,

$\tan(x) = \cot(\frac{\pi}{2} - x) \\ and \: \sin( {90}^{o} ) = 1$

Some important Trigonometry formula,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

know more about Trigonometry,

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