Answers

The Brainliest Answer!
2015-04-14T20:39:53+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
these are all simple exercises,  you need to just substitute the values of trigonometric ratios and simply the expressions.  that is all.



tan² A - Sin² A = Sin²A / Cos² A -  Sin² A
       = Sin² A sec²A - Sin²A
       = Sin ² A ( sec²A - 1)
       = sin² A  tan²A =  sin² A  sin²A  / cos²A
======================
ii
   multiply the two terms to get
   1+tan A+sec A+cot A+1+cotA SecA - CosecA - cosecA tan A - cosecA secA
       = 2 + tanA + secA +cosA/sinA + cosA/sinA *1/cosA - 1/sinA - 1/sinA*sinA/cosA - 1/sinA * 1/cosA
       = 2 + sinA/cosA + 1/cosA +CosA/sinA+ 1/sinA -1/sinA - 1/cosA - 1/sinA*1/cosA
     = 2 + sinA/cosA + cosA/sinA - 1/sinA * 1/cosA
   = 2 + (sin²A +cos²A - 1 ) / (sinA cosA)
  =  2
======================
      LHS    1/(cosecA- cotA) - 1/sin A
multiply numerator and denominator  with (coseA+ cotA)
           (cosecA + cotA)/ 1  - cosec A  = cot A 

       RHS      1/sinA  -  1/ (cosecA + cotA)
 multiply numerator and denominator with  (cosec A - cot A)

  cosec A -  (cosecA - cotA) / (cosec²A - cot²A)

  =  cot A

  LHS = RHS = cot A
========================

(cot A + tan B) / ( cot B + tan A)  = 
       = (cosA / sinA +  sin B / cosB )    /   (cosB/sinB + sin A/ cosA)
   =  (cosA cosB + sinA sin B) * CosA sin B /  [ (cosA cosB + sinA sinB) * sinA cos B ]
  = cot A    tan B
   as the summation term cancels.
 



2 5 2
these are all simple exercises, you need to just substitute the values of trigonometric ratios and simply the expressions. that is all.
click on thanks blue button above pls
yes sir that thanks one i clicked
sir look at commnet i posted plzzzzzzz