Question

In triangle ABC,right angled at c, in which AB =29 units , BC = 21 units and angle ABC=θ.determine the value of
(1) cos²θ + sin²θ
(2) cos²θ - sin²θ

Answer 1

we know, according to Pythagoras theorem ,
AB² = AC² +BC²

AC=√(AB² -BC²)

AC=√(29² -21² ) =20 unit .

sin∅ = AC/AB = 20/29
cos∅ =BC/AB = 21/29

(1) sin²∅ + cos∅ =?
sin²∅ +cos²∅ = (20²+21²)/29² = 29²/29² =1

(2) cos²∅ -sin²∅ =?

cos²∅ -sin²∅ =(21/29)² -(20/29)²

=(21² -20²)/29² =41/29² =41/841

Answer 2

ABC an triangle
90 at c
AB=29
BC=21
AC=√(AB^2-BC^2)
AC=√(29^2 -21^2)
AC=√400
AC=20
angle B is thita
Then base of riangle is BC
and AB is hypotenuos and AC is perpendicular
cos (thita)=BC÷AB
=21÷29=0.724
cos^2(thita)=0.524
sin^2(thita)=(AC÷AB)^2
=0.474
Cos^2(thita)+sin^2(thita)=0.524+0.474=0.998
cos^2(thita)-sin^2(thita)=0.524-0.474=0.050