Question

Prove that cot40 + tan40=2sec10

Answer 1

if you wannna ask that whether cot4x + tan4x = 2secx

is right or wrong.

i can tell you that this is wrong .

yes if you put x= 10° then it become your question and luckily the RHS and LHS are approximately equal but its luckily happened.

if you put x = 20 ° then it dosent satisfy the equation.

so i believe you have your answer.

Answer 2

Answer:

Step-by-step explanation:                                  [w.k.t means we konw that]                              

L.H.S :-

(sin40°/cos40°)+(cos40°+sin40°)

do LCM

then, (sin^2 40°+cos^2 40°) / (cos4°sin40°)

then, 1 / (cos40°sin40°)          [w.k.t, sin^2 θ +cos^θ =1]

then, 2 / 2(cos40°sin40°)       [multipling 2/2 with the above line]

then, 2 / sin 2 (40°)           [w.k.t , 2sinθcosθ = sin2θ]

then, 2 / sin80°

then, 2 cosec80°

then, 2 sec(90°-80°)

then, 2sec10°            

                          [proved]                                 done by----------

                                                                                            (Sayandeep Dutta)

                                                                                            [S.B.H.S -- SCIENCE]