Question

Using trigonometric identities and right triangles to find the exact values the following:

a) sin (2* cos^-1(2/5))

b) cos (sin^-1(1/4) + tan^-1(2))

Answer 1

Solution 10) given that sin (2005" ( } )) to solve this Let Cost (3)= 0 z = logo know that Now by right angle triangle, we Base COSA = Hypotenuse mu Perpendiculor 5 Hypotenuse 2 Base Put cost (3) = 0 in equation ☺ sin / 20) - We know that 2 sino coso sin (2A) asinA USA from the triangle = 293) sing = Peopendliwler 121 Hypotonuse 4T 25 so, sin ( 2605+13)) 4377 25

(6) given that Cos I sint () + ton/2)) So, to solve this Let sint (5) = 2 sinde we know that - Al- sina = Perpandiwlar Hypotenusa 115 and tont/2) = 4 2= tony 2 Ni- 11 tomy= Perpendiwlar Base we know that 5 2 and font (2) = y in equation Now put sin-'( 6) = x Cos(s+y) = Cosa cosy-sinn sing

From the first triangle value of osac, will be Cosze = Base Hypotenuse Cosa = 15 from the second triangle, value of smy and easy will be siny= perpendi wlar Hypotenuse siny 2 5 Base Cosy = Hypotenuse Cosy = 1/4 But all values (195) (+) - (1) (i) 2 115 455 455 115 - 2 455 So, Cos ( sintl #) + ternt 12)) √15 -2 45