consider triangle ABC right angled at C in which ab = 29 units, BC= 21 units and triangle abc = theta determine the values of cos square theta + sin square theta
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By Pythagoras theorem,
AB
2
=AC
2
+BC
2
⇒AC
2
=AB
2
−BC
2
⇒AC
2
=29
2
−21
2
=(29+21)(29−21)=50×8
⇒AC
2
=25×16
⇒AC=5×4=20 units
⇒cosθ=
AB
BC
=
29
21
,
sinθ=
AB
AC
=
29
20
⇒sin2θ+cos
2
θ=
29
2
21
2
+20
2
=
29
2
29
2
=1
⇒cos
2
θ−sin
2
θ=
29
2
21
2
−20
2
=
841
41
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