Prove the following

Asked by Apoorva | 14th Jun, 2017, 11:04: AM

Expert Answer:

begin mathsize 16px style 1.
fraction numerator 1 minus sinA space cosA over denominator cosA space open parentheses secA minus cosecA close parentheses end fraction cross times fraction numerator sin squared straight A minus cos squared straight A over denominator sin cubed straight A plus cos cubed straight A end fraction
using space secA space equals fraction numerator 1 over denominator cos space straight A space end fraction space and space cosec space straight A equals 1 over sinA
rightwards double arrow fraction numerator 1 minus sinA space cosA over denominator cosA space open parentheses begin display style 1 over cosA end style minus begin display style 1 over sinA end style close parentheses end fraction cross times fraction numerator open parentheses sinA minus cosA close parentheses open parentheses sinA plus cosA close parentheses over denominator open parentheses sinA plus cosA close parentheses open parentheses sin squared straight A plus cos squared straight A minus sinA space cosA close parentheses end fraction
On space simplifying space you space will space get space
rightwards double arrow fraction numerator sinA space cos space straight A over denominator cosA end fraction
rightwards double arrow sinA

2.
open parentheses secθ minus 1 close parentheses squared minus open parentheses tanθ minus sinθ close parentheses squared
convert space secθ space into space cosθ space also space tanθ space into space sin space and space cos space and space simplify

3.
tanA space plus space sinA space equals straight m comma space tanA minus sinA equals straight n
Put space this space in space the space straight m squared minus straight n squared space and space simplify.
Try space to space solve space these space two space questions. space If space you space will space have space doubt space while space solving space
please space post space it space again space with space snapshot space of space your space steps space straight I space will space guide space you space further. end style

Answered by Sneha shidid | 14th Jun, 2017, 12:06: PM