Question

6 tan square theta -6 sec square theta =

Answer 1

Answer :

-6

Explanation:

Here I am using A instead of theta.

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We know the algebraic identity:

sec²A - tan²A = 1

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Now ,

6tan²A - 6sec²A

= 6( tan²A - sec²A)

= -6(sec²A - tan²A)

= -6 × 1

= -6

••••

Answer 2

We have to find the value of :

$6 { \tan }^{2} \alpha - 6 { \sec}^{2} \alpha$

As we know that :

${ \sec }^{2} \alpha = 1 + { \tan}^{2} \alpha \\ \\ = > { \tan }^{2} \alpha - { \sec }^{2} \alpha = - 1.....(1)$

So,

$6 { \tan }^{2} \alpha - 6 { \sec }^{2} \alpha \\ \\ = > 6( { \tan}^{2} \alpha - { \sec }^{2} \alpha ) \\ \\ = > 6 \times ( - 1) \\ \\ = > - 6 \: \: \: \: \: \: \: \: \: \: [ \: From \: equation \: (1) \:]$