Sec 16° cosec 74° - cot 74° tan 16°

1.

Step-by-step explanation:

sec 16° cosec 74° - cot 74° tan 16°

= 1/ cos 16 * 1/ sin 74 - 1/tan 74 * tan16

= 1/ cos16 sin 74 -  cos74/ sin74 *  sin 16 / cos 16

Now cos 16 = sin 74  and sin 16 = cos 74  (supplementary angles) so:

= 1 / cos^2 16   - sin 16/cos 16 * sin 16 / cos 16

=( 1 - sin ^2 16 )/ cos^2 16

= cos^2 16 / cos^2 16

= 1.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation: