Question

what is the value of 3tan²θ - 3sec²θ. by 4​

Answer 1

Answer:

Let's trigonometric identities for we know that

tan ²Φ - sec²Φ = 1

In the given question ,

3 tan ²Φ - 3 sec²Φ = 4

Taking 3 common,

3 (tan ²Φ- sec ²Φ)/4

Using identities,

3(1)/4=3/4 is the answer

Answer 2

$\pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: we \: know \: that \\ \\ \bf \: {sec}^{2} \theta - {tan}^{2} \theta = 1 \\ \\ \bf \implies \: - ( {tan}^{2} \theta - {sec}^{2}\theta) = 1 \\ \\ \bf \implies \: {tan}^{2} \theta - {sec}^{2}\theta = - 1 \: \: \: - - (1) \\ \\ \orange{{\boxed{\begin{array}{cc} \maltese \bf \: now \: given \\ \\ \bf \: \frac{3 {tan}^{2}\theta - 3 {sec}^{2}\theta }{4} \\ \\ \bf = \frac{3( {tan}^{2}\theta - {sec}^{2} \theta)}{4} \\ \\ \bf = \frac{3 \times ( - 1)}{4} \: \: \: \{ \sf \: by \: eqn .(1) \} \\ \\ = - \frac{3}{4} \end{array}}}} \end{array}}}}$