Question

simplify (1+tan²R) (1+sinR)(1-sinR)

Answer 1

the question is from trigonometric ratios and can be easily solved by using the identities of the trigonometric ratios.

the three and it is which are common in class 10 can be used in order to solve this. also, we can use various algebraic identities to solve the following question because this question includes some algebraic identities.

$(1 + { \tan(r) }^{2} )(1 + \sin(r) )(1 - \sin(r) ) \\ \\ = (1 + { \tan(r) }^{2} )(1 - { \sin(r) }^{2} ) \\ \\ = ( { \sec(r) }^{2} )( { \cos(r) }^{2} ) \\ \\ = {( \sec(r) \cos(r) )}^{2} \\ \\ = {1}^{2} = 1$

the identities which are used are as follows including the algebraic identities :-

A) 1 + tan²R = sec²R

B) 1 - sin²R = cos²R

C) cosR * secR = 1

D) (a+b) (a-b) = a² - b²