sin^2 70 + cos ^ 110= 1
Answers
Step-by-step explanation:
sin
2
70
∘
+cos
2
110
∘
=1
EVALUATION
\sf{ { \sin}^{2} {70}^{ \circ} + { \cos}^{2} {110}^{ \circ} \: }sin
2
70
∘
+cos
2
110
∘
= \sf{ { \sin}^{2} {70}^{ \circ} + { \big( \cos {110}^{ \circ} \big)}^{2} \: }=sin
2
70
∘
+(cos110
∘
)
2
= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ \cos ( {180}^{ \circ} - {70}^{ \circ}) \bigg] }^{2} \: }=sin
2
70
∘
+[cos(180
∘
−70
∘
)]
2
= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ \cos ( 2 \times {90}^{ \circ} - {70}^{ \circ}) \bigg] }^{2} \: }=sin
2
70
∘
+[cos(2×90
∘
−70
∘
)]
2
= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ - \cos {70}^{ \circ} \bigg] }^{2} \: }=sin
2
70
∘
+[−cos70
∘
]
2
= \sf{ { \sin}^{2} {70}^{ \circ} + { \cos}^{2} {70}^{ \circ} \: }=sin
2
70
∘
+cos
2
70
∘
= \sf{1 \: \: \: \: \: ( \: \because { \sin}^{2} \theta + { \cos}^{2} \theta \: = 1 \: )}=1(∵sin
2
θ+cos
2
θ=1)