Question

show that cos square 45 degree + theta + cos square 45 degree minus theta upon tan 60 degree + theta tan 30 degree minus theta equals to 1​

Answer 1

Step-by-step explanation:

Given Show that cos square 45 degree + theta + cos square 45 degree minus theta upon tan 60 degree + theta tan 30 degree minus theta equals to 1

• Given cos ^2 (45 + theta ) + cos^2 (45 – theta) / tan (60 + theta) tan (30 – theta)
•    = sin^2 (90 – (45 + theta) + cos^2 (45 – theta) / cot (90 – (60 + theta) tan (30 – theta)
•   = sin ^2 (45 – theta) + cos^2 (45 – theta) / cot (30 – theta) tan (30 – theta)
•   = 1 / 1  (because sin^2 theta + cos^2 theta = 1 and tan theta.cot theta = 1)
•  = 1

Reference link will be

https://brainly.in/question/2383300

Answer 2

The given trigonometrical function is proved  .

Step-by-step explanation:

Given as :

The trigonometrical function

To prove : $\dfrac{Cos^{2}(45^{\circ}+\Theta ) + Cos^{2}(45^{\circ}-\Theta ) }{[Tan (60^{\circ}+\Theta )] [Tan (30^{\circ}-\Theta )]}$   =  1

According to question

From the left hand side of given equation

$\dfrac{Cos^{2}(45^{\circ}+\Theta ) + Cos^{2}(45^{\circ}-\Theta ) }{[Tan (60^{\circ}+\Theta )] [Tan (30^{\circ}-\Theta )]}$ = $\dfrac{Sin^{2}([90^{\circ}-(45^{\circ}+\Theta )] + Cos^{2}(45^{\circ}-\Theta ) }{[Cot[90^{\circ}- (60^{\circ}+\Theta )] [Tan (30^{\circ}-\Theta )]}$

                                          ∵ Sin ( 90° - Ф ) = Cos Ф , Cot ( 90° - Ф ) = Tan Ф

  Or,                                            = $\dfrac{Sin^{2}((45^{\circ}-\Theta )] + Cos^{2}(45^{\circ}-\Theta ) }{[Cot(30^{\circ}-\Theta )] [Tan (30^{\circ}-\Theta )]}$  

  Or,                                           =  $\dfrac{Sin^{2}((45^{\circ}-\Theta )] + Cos^{2}(45^{\circ}-\Theta ) }{ \dfrac{[Tan (30^{\circ}-\Theta )]}{[Tan (30^{\circ}-\Theta )]}}$                

                                            ∵  Cot Ф =  $\dfrac{1}{Tan \Theta }$

   Or,                                          =  $\dfrac{1}{1}$            ( ∵ Sin²Ф + Cos²Ф = 1 )

∴  $\dfrac{Cos^{2}(45^{\circ}+\Theta ) + Cos^{2}(45^{\circ}-\Theta ) }{[Tan (60^{\circ}+\Theta )] [Tan (30^{\circ}-\Theta )]}$ = 1  

So, Left hand side = Right hand side   , proved

Hence, The given trigonometrical function is proved  . Answer