Question

Prove that sin²α + cos²α = 1 and " title="\frac{1}{cos^{2}\alpha }" alt="\frac{1}{cos^{2}\alpha }" align="absmiddle" class="latex-formula"> = 1 + tan²α

Answer 1

Answer:

See Explanation

Step-by-step explanation:

${ \sin}^{2} \alpha + { \cos}^{2} \alpha = 1 \\ \\ LHS = { \sin}^{2} \alpha + { \cos}^{2} \alpha \\ \\ = \cancel {\sin}^{2} \alpha + { 1 -\cancel{ \sin}}^{2} \alpha \\ \\ = 1 \\ \\ = RHS \\ \\ \\ \frac{1}{ { \cos}^{2} \alpha } = 1 + { \tan}^{2} \alpha \\ \\ LHS = \frac{1}{ { \cos}^{2} \alpha } \\ \\ = { \sec}^{2} \alpha \\ \\ = 1 + { \tan}^{2} \alpha \\ \\ = RHS$