Question

How do I do this??!.​

Answer 1

 What is trigonometry?

Trigonometry is the branch of geometry that gives the relationship between the angles and sides of a triangle.

c) proof. if cos∅ = $\frac{x}{\sqrt{x^{2} + y^{2} } }$,  then x = adjacent, $\sqrt{x^{2} + y^{2} }$ = hypotenuse

  To solve for opposite, since it is a right angle triangle

   $hypotenuse^{2}$ = $opposite^{2}$ + $adjacent^{2}$

  $(\sqrt{x^{2} + y^{2} }) ^{2}$ = $opposite^{2}$ + $x^{2}$

  $opposite^{2}$ = $x^{2}$ +$y^{2}$ -$x^{2}$

   opposite = y

xsin∅ = x$(\frac{y}{\sqrt{x^{2} + y^{2} } })$ = $\frac{xy}{\sqrt{x^{2} } + y^{2} }$

ycos∅ =  $\frac{xy}{\sqrt{x^{2} } + y^{2} }$

Therefore xsin∅ = ycos∅

d) 41 sin∅ = 40

   sin∅ = 40/41

   solving for adjacent = 9

    tan ∅ = opp/adj = 40/9

$\frac{tan \alpha }{tan^{2}\alpha - 1 }$ = 40/9 ÷ $(\frac{40}{9} )^{2}$ - 1 = 40/9  ÷ 1600/81 - 1

                                         = 40/9  ÷ 1519/81 = 40/9 x 81/1519 = 360/1519

e) 1 - cos ∅ = 1/2

    cos ∅  = 1 - 1/2 = 1/2

   ∅ = cos inverse of 0.5 = 60°

   tan 60 = $\sqrt{3}$    $tan^{2} 60$ = 3, sin 60 = $\frac{\sqrt{3} }{2}$ $sin^{2} 60$ = 3/4

      $tan^{2} 60$ +  4$sin^{2} 60$ = 3 + 4(3/4) = 3 + 3 = 6

Learn more about trigonometry: brainly.com/question/24349828

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