MathematicsIf 4𝑡𝑎𝑛θ = 3 then evaluate, 4sinθ−cosθ+14sinθ+cosθ−1

If 4𝑡𝑎𝑛θ = 3 then evaluate, 4sinθcosθ+14sinθ+cosθ1

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    Solution:

     

     

     

     

     

     

     

     

     

     

     

    It is given that 4𝑡𝑎𝑛θ = 3

     i.e tanθ=34tanθ= opposite side of θ adjacent side of θ

    By hypotenuse rule

    AC2=BC2+AB2AC2=42+32AC2=16+9AC2=25AC=5

     Now, sinθ= opposite side of θ hypotenuse sinθ=ABACsinθ=35Cosθ= adjacent side of θ hypotenuse 

    cosθ=45 Now ,4sinθcosθ+14sinθ+cosθ1=43545+1435+451=85+11651=135115=1311 

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