Complete the proof of the identity by choosing the Rule that justifies each step. (1- cos x) so
secx sin tan
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( 1 - cos²x ) secx

=> sin²x . secx

Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .

=> sin²x [ 1/cosx ]

Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .

=> sinx [ sinx/cosx ]

Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].

=> sinx tanx

Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .

step-by-step explanation:

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).