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Complete the proof of the identity by choosing the Rule that justifies each step.
(1- cos x) so
secx sin tan
To see a detailed description of a Rule, select the More Information Button to the right of the Rule,

Complete the proof of the identity by choosing the Rule that justifies each step 1 cos x so secx sin tan To see a detailed description of a Rule select the More class=

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Answer :-

( 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 .

The proof of the identity that justifies that ( 1 - cos²x ) secx equals sinx(tanx) has been described below with statements and rules.

Statement 1; ( 1 - cos²x ) secx

This is given

Statement 2; sin²x · secx

Rule 1;  From trigonometric identities, we know that;

sin²x + cos²x = 1,

Thus; cos²x = 1 - sin²x

Thus; ( 1 - cos²x ) secx = sin²x · secx

Statement 3; sin²x (1/cosx)

Rule 2;  The rule here according to trigionometric identities is that; secx = 1/cosx. Thus; secx = 1/cosx .

Statement 4; sinx (sinx/cosx )

Rule 3;  The rule here is that sin²x can be expressed as (sinx * sinx)

Thus, we have; sinx . sinx (1/cosx) = sinx (sinx/cosx ).

Statement 5; sinx(tanx)

Rule 4;  The rule here is that; sinx/cosx = tanx.

Thus;  sinx (sinx/cosx ) gives us sinx(tanx)

Read more at; https://brainly.com/question/24836845

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