ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

ICSE / ISC eBooks

Example - 1. Prove that :  cosA /(1 – sinA) + cosA / (1 + sinA) = 2 secA.

Solution :- LHS = cosA / (1 – sinA) + cosA / (1 + sinA)
                               cos A (1 + sinA) + cosA (1 – sinA)
                          = ---------------------------------------------- 
                                         (1 – sinA)(1 + sinA)
                               cosA + cosA sinA + cosA – cosA sinA 
                         = --------------------------------------------------
                                                     1 – sin²A
                          = 2cosA / cos²A  =  2/ cosA  = 2secA = RHS.

Example – 2  Prove that : sec²A + cosec²A  =  sec²A cosec²A

Solution :-                      LHS  =  sec²A + cosec²A

=  1/cos²A + 1/sin²A

=  (sin²A + cos²A)/cos²A sin2A         [sin²A + cos²A = 1]

=  1/cos²A sin²A

=  1/cos²A ×1/sin²A

=  sec²A cosec²A  =  RHS.