poudelbibek73
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Prove this please
Optional Math




Cos2A =
[tex] \frac{( \cot\alpha - \tan\alpha ) }{( \cot\alpha + \tan\alpha ) } [/tex]

​

Sagot :

bunnuika

Step-by-step explanation:

proof from r.h.s to l.h.s

(cot(a)-tan(a))(cot(a)+tan(a))

cot(a)=cos(a)/sin(a)

tan(a)=sin(a)/cos(a)

(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)

=cos²(a)-sin²(a)/sin(a)cos(a)

from trigonometry identity cos²(a)-sin²(a)=cos2(a)

so we have cos2(a)/sin(a)cos(a)

(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)

=cos²(a)+sin²(a)/cos(a)sin(a)

from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)

(cot(a)-tan(a)) ÷(cot(a)+tan(a))

=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)

=cos2(a)/cos(a)sin(a) * cos(a)sin(a)

=cos2(a)

proved

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.