Question

6. If sec^2teta (1+sin teta) (1-sin teta) = k, find the value of k​

Answer 1

Given:

$\star \bold{ { \sec}^{2} \theta \: (1 + \sin \theta)(1 - \sin \theta) = k}$

To find :

• The value of k .

Solution :

$\implies \: { \sec}^{2} \theta \: (1 + \sin \theta \: )(1 - \sin \theta) \\ \\ \implies \: { \sec}^{2} \theta \: ( {1}^{2} - { \sin}^{2} \theta) \\ \\ \implies \: { \sec}^{2} \theta(1 - { \sin}^{2} \theta) \\ \\ \implies \: { \sec}^{2} \theta \: ( \cos ^{2} \theta) \\ \\ \implies \: 1$

Hence , the value of K is 1.

• Formula :

$\star \: \bold{ { \sin}^{2} \alpha + { \ \cos}^{2} \alpha = 1} \\ \\ \star \: \bold{ { \sec}^{2} \alpha - { \tan}^{2} \alpha = 1} \\ \\ \star \: \bold{ { \csc }^{2} \alpha - { \cot}^{2} \alpha = 1} \\ \\ \star \: \sec \alpha \times \cos\alpha = 1 \\ \\ \star \: \tan( \alpha ) \times \cot( \alpha ) = 1 \\ \\ \star \: \: \sin( \alpha ) \times \csc( \alpha ) = 1$

Answer 2

Step-by-step explanation:

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